Question 1 : A body crosses the topmost point of a vertical circle with critical speed. What will be its centripetal acceleration when the string is horizontal:

Question 4 : If a disc starting from rest acquires an angular velocity of $240$ revolution/ min in $10\ s$, then its angular acceleration will be

Question 5 : Find the unit vectors which are perpendicular to both the vector $ i+4j $ and $ 2i+4j+3k. $<br>

Question 6 : If $ {P} =&#160; \vec{A} + \vec{B} $ and $Q = \vec{A} - \vec{B} $ if magnitude of $P$ and $Q$ are equal then angle between $A$ and $B$ is ?

Question 7 : A body is projected obliquely from the ground such that its horizontal range is maximum. If the change in its linear momentum, as it move from half the maximum height to maximum height, is $P$, the change in its linear momentum as it travels from the point of projection to the landing point on the ground will be

Question 8 : If a particle is thrown vertically upwards, then its velocity so that it covers same distance in 5th and 6th second would be

Question 9 : &#160;A cannon ball of mass $500 g$ is fired with a speed of $15 m s^{-1}$. Find its momentum.

Question 10 : The momentum of a toy bus of $0.01\ kg$ moving with a velocity of $5\ m/s$ is:

Question 11 : A block of mass $M$ at the end of the string is whirled round a vertical circle of radius $R$. The critical speed of the block at the top of the swing is

Question 12 : A train weighting ${ 10 }^{ 7 }N$ is running on a level track with uniform speed of $36\ km/h$. The frictional force is $0.5\ kgf$ per quintal. What is the power of the engine?

Question 13 : A ball of mass $m$ is attached with the&#160;string of length $R$,&#160;rotating in circular motion, with instantaneous velocity $v$&#160;and centripetal acceleration $a$.Calculate the centripetal acceleration of the ball if the length of the string is doubled?

Question 14 : A block of mass M is pulled along a horizontal rough surface by a rope of mass m by applying a force F at one end of the rope. f is the friction between block and the surface. The force which the rope exerts on the block is:

Question 15 : A $4g$ bullet is fired horizontally with a speed of $300 m/s$ into $0.8 kg$ block of wood, which is&#160;at rest on a table. If the coefficient of friction between the block and the table is $0.3$, how far will the block slide approximately?

Question 16 : A car taken a turn along a curved road of radius $40$ m and the angle of banking of the road is $\displaystyle {45} ^ {o} $. At what maximum speed can the car be driven so that it may not skid. $\displaystyle (g\ =&#160;{10\ ms} ^{-2} $).

Question 17 : A body of mass $m=10^{-2}\ kg$ is moving in medium and experiences a frictional force $F=-kv^2$. Its initial speed is $v_0=10\ ms^{-1}$. If, after $10\, s$, its energy is $\dfrac{1}{8}mv_0^2$, the value of $k$ will be :

Question 18 : A ball tied to the end of the string swings in a vertical circle under the influence of gravity.

Question 19 : A bowling ball is rolling westward and slowing down as it approaches the end of the alley. The direction of the bowling ball's acceleration is :

Question 20 : Three bodies $A, B$ and $C$ are moving in a straight line in the same direction such that relative velocity of $A$ w.r.t $B$ is $2m/s$, relative velocity of $B$ w.r.t $C$ is $5m/s$.<br/>Find the relative velocity of $C$ w.r.t $A$.&#160;

Question 21 : An elevator is moving up with $2.5 m{ s }^{ -1 }$. A bolt in the elevator ceiling $3\ m$ above the elevator falls. How long (in seconds) does it take for the bolt to fall on the floor of the elevator?<br>

Question 22 : A stone is projected up with a velocity of $4.9\ m/s$ from the top of a tower and it reaches the ground after 3 s. Then the height of that tower is<br/>

Question 23 : Equation of motion of a particle moving in straight line is given by $x=\dfrac{1}{2}vt$ then its acceleration is&#160;

Question 24 : A bullet travelling horizontally loses ${\dfrac{1}{20}^{th}}$ of its velocity while piercing a wooden plank. Number of such planks required to stop the bullet is:

Question 25 : The driver of a train moving with a constant speed $v_1$ along a straight track sights another train at a distance d ahead of him on the same track moving in the same direction with a constant speed $v_2$. He at once applies the brakes and gives his train a constant retardation f. There will be a collision of the trains if:<br>

Question 26 : A ball is thrown with a velocity of $6\mathrm { m } / \mathrm { s }$ vertically from a height $\mathrm { H } = 3.2 \mathrm { m }$ above a horizontal floor. If it rebounds back to same height then coefficient of restitution $e$ is $\left[ 9 = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right]$

Question 27 : David drives half the distance from $A$ to $B$ at $40$ miles per hour and the other half of the distance at $60$ miles per hour. Calculate her average rate of speed, in miles per hour, for the entire trip.

Question 28 : A stone drop from height 'h' reaches at earth surface in 1 sec. If the same stone is taken to moon and dropped freely from height h, then it will reach the surface of moon in ..... sec

Question 29 : A ball moving with a velocity v strikes a wall moving toward the ball with a velocity u. An elastic impact lasts for t sec. Then the mean elastic force acting on the ball is

Question 30 : The coefficient of restitution (e) for a perfectly elastic collision is<br>

Question 31 : &#160;A body $P$ &#160;moving with a velocity of $20$ms$^{-1}$&#160;collides with another body $Q$ of same mass at rest. After collision $P$ comes to rest. What is the velocity of the body $Q$ ?<br/>

Question 32 : <p>Two pendulum bobs of mass $m$ and&#160; $2\ m$ collide elastically at the lowest point in their motion. If both the balls are released from height $H$ above the lowest point. The velocity of the bob of mass $m$ just after collision is :</p>

Question 33 : Energy possessed by a body by virtue of its motion is :

Question 34 : A block of mass $2.0\ kg$ is pushed down an inclined plane of inclination $37^{o}$ with a force of $20\ N$ acting parallel to the incline. It is found that the block moves on the incline with an acceleration of $10\ m/s^{2}$.&#160;If the block&#160;started from rest, find the work done (a) by the applied force in the first second&#160;<br/>

Question 35 : Two balls of equal mass undergo head on collision while each was moving with speed $6\ m/s$. If the coefficient of restitution is $\dfrac{1}{3}$, the speed of each ball after impact will be<br>

Question 36 : A particle is moving along with X-axis such that its acceleration is proportional to the displacement from the equilibrium position and they are in the same direction. The displacement x( t) is given by

Question 37 : A collision occurs between two identical balls each of mass $m$ , moving with velocity $ \overrightarrow { u_1 } $ and $ \overrightarrow { u_2 } $ , colliding head-on. The coefficient of resolution is $0.5$ The energy lost in the collision is :

Question 38 : A person pulls a bucket of water from a well of depth $h$. If the mass of uniform rope is $m$ and that of the bucket full of water is $M$, then work done by the person is:

Question 39 : The resultant of two forces 3P and 2P is R. If the first force is doubled then the resultant is also doubled. The angle between the two forces is

Question 40 : A particle moving with kinetic energy = 3J makes an elastic headon collision with a stationary particle which has twice its mass. During the impact.

Question 41 : Assume that a satellite is revolving around Earth in a circular orbit almost close to the surface of Earth. The time period of revolution of satellite is $( $Radius of earth is 6400 km, $g =$ 9.8 $ms^{-2})$<br>

Question 42 : An earth's satellite is moving in a circular orbit with a uniform speed v. If the gravitational force of the earth suddenly disappears, the satellite will:-

Question 43 : Two planets A, B have their radii in the ratio $ 2: 5$ and densities in the ratio $ 1: 6$ respectively. Choose the correct statement(s)

Question 44 : The ratio of acceleration due to gravity at a height h above the surface of the earth and at a depth h below the surface of the earth h &lt; radius of earth

Question 45 : Fifteen joules of work is done on object A so that only its gravitational potential energy changes. Sixty joules of work is done on object B (same mass as object A) so that only its gravitational potential energy changes.<br>How many times does the height of object B change compared to the height change of object A, as result of the work done?

Question 46 : There are two planets. The ratio of radius of the two planets is $k$ but ratio of acceleration due to gravity of&#160;both planets is $g$. What will be the ratio of their escape velocity?

Question 47 : A planet in a distant solar system is $10$ times more massive than the earth and its radius is $10$ times smaller. Given that the escape velocity from the earth is $11 km$ $\mathrm{s}^{-1}$, the escape velocity from the surface ofthe planet would be<br/>

Question 48 : A man weighs $60kg$ at earth surface. At what height above the earth's weight become $30kg$,&#160;Given radius of earth is $6400km$:

Question 49 : A tunnel is dug along a diameter of the earth. If ${ M }_{ e }$&#160;and ${ R }_{ e }$&#160;are the mass and radius, respectively, of the earth, then the force on a particle of mass ${ m }$&#160;placed in the tunnel at a distance ${ r }$&#160;from the centre is :

Question 50 : The linear velocity of a particle at the N- pole of&#160;the earth due to its rotation is:<br/>

Question 51 : A particle is moving with uniform speed along a&#160;circle of radius $20$ cm. If angular velocity of particle&#160;is $5\ rad s^{&#8211;1}$ then its speed is:<br/>

Question 52 : A uniform metre rule of weight $10gf$ is pivoted at its $0$ mark. How can it be made horizontal by applying a least force?<br/>

Question 53 : A thin rod of mass $96 &#160;g$ and of length $1 &#160;m$ is&#160;made to rotate about an axis perpendicular to&#160;the length of rod passing through a point at a&#160;distance $25 &#160;cm$ from one end of rod. The moment&#160;of inertia of that rod is:<br/>

Question 54 : A sphere is rolling down an inclined plane without slipping. The ratio of rotational energy to total kinetic energy is<br>

Question 55 : AU the particles of a system are situated at a distance r from the origin. The distance of the centre of mass of the system from the origin is :

Question 56 : A child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal track. If the&#160; child starts running towards the other end of the trolley with a speed $u$. The centre of mass of the system (trolley+child) will move with a speed:

Question 57 : A bowling ball of uniform density is projected along a horizontal with a velocity $v_{0}$ so that it initially slides without rolling. The ball has mass $m$ and coefficient of static friction $\mu _{d}$ with the floor. Ignore air-friction. Let $t$ be the time at which the ball begins to roll without sliding and $v$ be the velocity of the ball when this happens. Then:

Question 58 : A uniform chain of mass $M$ and length $L$ is held vertically in such a way that its lower end just touches the horizontal flour. The chain is released from rest in this position. Any portion of chain that strikes the floor comes to rest. Assuming that the chain does not form. Then:<br>

Question 59 : When a force of $1$N acts on $1$kg mass at rest for $1$s, its final momentum is $P$. When $1$N force acts on $1$kg mass at rest through a distance $1$m, its final momentum is $P'$. The ratio of $P$ to $P'$ is:

Question 60 : A steel cable with a radius $2cm$ supports a chairlift at a ski area. If the maximum stress is not to exceed ${ 10 }^{ 8 }N\quad { m }^{ -2 }$, the maximum load the cable can support is

Question 61 : The temperature of a wire is doubled. The Young's modulus of elasticity will ?

Question 62 : Elongation of a wire under its own weight is&#160;independent of :

Question 63 : A wire of length L and of cross-sectional area A is made of a material of Young's modulus Y. The work done in stretching the wire by an amount $x$ is given by :

Question 64 : The length of a metal is $l_1$ when the tension in it is $T_1$ and is $l_2$ when the tension is $T_2$. The original length of the wire is&#160; :<br/>

Question 65 : A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, $\left(\displaystyle\frac{dr}{r}\right)$, is?

Question 66 : A wire elongates by $1 mm$ when a load W is hanged from it. lf the wire goes over a pulley and two weights $\mathrm{W}$ each are hung at the two ends, the elongation of the wire will be (in mm):<br/>

Question 67 : An increase in pressure required to decreases the $200$ litres volume of a liquid by $0.004\%$ in the container is(Bulk modulus of the liquid $=2100$ MPa).

Question 68 : A liquid is contained in a vessel. The liquid-solid adhesive force is very weak as compared to the cohesive force in the liquid. The shape of the liquid surface will be:

Question 69 : Water is flowing through a very narrow tube. The velocity of water below which the flow remains a streamline flow is known as:

Question 71 : Due to air a falling body faces a resistive force proportional to square of velocity $v$, consequently its effective downward acceleration is reduced and is given by $a = g - kv^{2}$ where $k = 0.002m^{-1}$. The terminal velocity of the falling body is (in m/s)<br/>

Question 72 : A flat plate is placed normal to a discharging jet&#160;of water. The jet discharges water at the rate of&#160;0.2 $m^{3}$s$^{-1}$ and at a speed of 18 ms$^{-1}$. The force on&#160;the plate due to the jet, if the collision is inelastic&#160;is:

Question 73 : In a cylindrical vessel containing liquid of density $\rho$, there are two holes in the side walls at heights of $h_1$ and $h_2$ respectively such that the range of efflux at the bottom of the vessel is same. Find the height of a hole, for which the range of efflux would be maximum.

Question 74 : Three containers are used in a chemistry lab. All containers have the same bottom area and the same height. A chemistry student fills each of the containers with the same liquid to the maximum volume. Which of the following is true about the pressure on the bottom in each container?

Question 75 : In which one of the following cases will the liquid flow in a pipe be most streamlined

Question 77 : An electric kettle takes 4 A current at 220 V.<br>How much time will it take to boil 1 kg of water<br>from temperature <br>$ 20^{0}C ?$ The temperature of<br>boiling water is <br>$ 100^{0}C ?$<br><br><br>

Question 78 : For a cube and a sphere made of same material, what should be the ratio of the side of the cube to the radius of the sphere such that both of them have the same thermal capacity?<br/>

Question 79 : Solar radiation is found to have an intensity maximum neat the wavelength range of 470 nm. Assuming the surface of sun to be perfectly absorbing (a = 1), calculate the temperature of solar surface.

Question 80 : Parallel rays of light of intensity $I = 912 Wm^{-2}$ are incident on a spherical black body kept in surroundings of temperature $300$ K.Take Stefan-Boltzmann constant $\sigma =5.7 \times { 10 }^{ -8 } W{ m }^{ -2 }{ K }^{ -4 }$ and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to :<br/>

Question 81 : <br>The resistance of platinum wire is 2.4 ohms at $0^{\mathrm{o}}\mathrm{C}$ and 3.4 ohms at $100^{\mathrm{o}}\mathrm{C}$. lf the resistance at $\mathrm{t}^{\mathrm{o}}\mathrm{C}$ is 4 ohms then the temperature t is equal to<br><br><br>

Question 82 : <p class="wysiwyg-text-align-left">Two identical containers each of volume V$_{0}$ are joined by a small pipe. The containers contain identical gases at temperature T$_{0}$ and pressure P$_{0}$. One container is heated to temperature 2T$_{0}$ while maintaining the other at the same temperature. The common pressure of the gas is P and n is the number of moles of gas in container at temperature 2T$_{0}$.</p>

Question 83 : Two bodies $A$ and $B$ have thermal emissivities&#160;of $0.01$ and $0.81$ respectively. The outer&#160;surface areas of the two bodies are the&#160;same and&#160;radiate energy at the&#160;same rate. The wavelength $\lambda&#160;_{B}$, corresponding&#160;to the maximum spectral radiancy in the&#160;radiation from $B$, is shifted from the wavelength&#160;corresponding to the maximum spectral&#160;radiancy in the radiation from $A$ by $1.00\mu&#160;m$. If the temperature of $A$ is $5802$ K,

Question 84 : Which of the following is/are the reason of the irreversibility of process?

Question 85 : A 60J of heat is added to the system, resulting in 15J of work being done by the system. The remaining 45J of heat is released. Find out the efficiency of the system? <br/>

Question 86 : A Carnot engine has an efficiency of $1/6$. When the temperature of the sink is reduced by $62^o C$, its efficiency is doubled. The temperatures of the source and the sink are, respectively

Question 87 : An ideal heat engine working between temperatures $T_1$ and $T_2$ has an efficiency $\eta $ . The new efficiency if the temperatures of both the source and sink are doubled, will be

Question 88 : A rigid diatomic ideal gas undergoes an adiabatic process at room temperature,. The relation between temperature and volume of this process is $TV^x$ = constant, then $x$ is :

Question 89 : $200\ g$ mass of a certain metal at $83^{\circ}C$ is immersed in $300\ g$ of water of $30^{\circ}C$. Final temperature of combination is $33^oC$.Calculate the specific heat capacity of metal. Assume that the specific heat capacity of water is $4.2 J g^{-1} K^{-1}$

Question 91 : 4.0 kg of a gas occupies 22 . 4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 $J K ^ { - 1 }$ $m o l ^ { - 1 }$ If the speed of sound in this gas at NTP is 952 $m s ^ { - 1 }$ then the heat capacity at constant pressure is (Take gas constant R = 8.3 $J K ^ { - 1 }$ $m o l ^ { - 1 }$

Question 92 : $300$ gm of water at $25^o$C is added to $100$gm of ice at $0^oC$ . Final temperature of the mixture is:

Question 94 : The number of gas molecules striking per second per square meter of the top surface of a table placed in a room at $20^o$C and $1$ atmospheric pressure is of the order of($k_B=1.4\times 10^{-23}J/K$, and the average mass of an air molecule is $5\times 10^{-27}$kg)

Question 95 : The poisson's ratio for $O_2$ is $1.4$. Which of the following are correct for $O_2$?

Question 96 : <p class="wysiwyg-text-align-left">Two identical containers each of volume V$_{0}$ are joined by a small pipe. The containers contain identical gases at temperature T$_{0}$ and pressure P$_{0}$. One container is heated to temperature 2T$_{0}$ while maintaining the other at the same temperature. The common pressure of the gas is P and n is the number of moles of gas in container at temperature 2T$_{0}$.</p>

Question 97 : Relation between pressure ($P$) and energy density ($E$) of an ideal gas is-

Question 98 : The volume of mole of a prefect gas at NTP is&#160;______.

Question 99 : <p class="wysiwyg-text-align-left">A closed vessel&#160;contains a mixture of two gases Neon &amp; Argon the total&#160;mass of mixture is 28 gm.The partial pressure due to Argon and neon are 4atm and 12atm respectively.The mass of individual&#160;gases in vessel is$(M_{neon}=20,M_{argon}=40,R=8.3J/mol-k)$</p>

Question 100 : An ideal gas is taken from the state A(pressure $P_0$, volume $V_0$) to the state B (pressure $P_0/2$, volume $2V_0$) along a straight line path in the P-V diagram. Select the correct statement(s) from the following.