Question 1 : A point sized sphere of mass $'m'$ is suspended from a point using a string of length $'l'$. It is pulled to a side till the string is horizontal and released. As the mass passes through the portion where the string is vertical, magnitude of its angular momentum is:

Question 2 : A stationary body explodes into two fragments of masses ${m}_{1}$ and ${m}_{2}$. If momentum of one fragment is $p$, the minimum energy of explosion is

Question 3 : Two horizontal circular discs of different radii are free to rotate about their central axes. One disc is given some angular velocity and the other is stationary. Their rims are now brought in contact. There is friction between the rims. Correct statement from the following is:

Question 4 : A disc of mass $100\ g$ and radius $10\ cm$ has a projection on its circumference. The mass of projection is negligible. A $20\ g$ bit of putty moving tangential to the disc with a velocity of $5\ m\ s^{-1}$ strikes the projection and sticks to it. The angular velocity of disc is

Question 5 : A man standing on a platform holds weight in his outstreached arms. The system rotates freely about a central vertical axis. If he now draws the weights inward close to his body

Question 6 : A circular platform is mounted on a vertical frictionless axle. Its radius is $r=2m$ and its moment inertia is $I=200kg$ ${m}^{2}$. It is initially at rest. A $70kg$ man stands on the edge of the platform and begins to walk along the edge at speed ${v}_{0}=10{ms}^{-1}$ relative to the ground. The angular velocity of the platform is<br>

Question 7 : A disc of moment of inertia $'I_{1}'$ is rotating in horizontal plane about an axis passing through a centre and perpendicular to its plane with constant angular speed $'\omega_{1}'$. Another disc of moment of inertia $'I_{2}'$ having zero angular speed is placed coaxially on a rotating disc. Now both the discs are rotating with constant angular speed $'\omega_{2}'$. The energy lost by the initial rotating disc is

Question 8 : A thin circular ring of mass $M$ and radius $r$ is&#160;rotating about its axis with constant angular&#160;velocity $\omega$. Two objects each of mass $m$ are&#160;attached gently to the opposite ends of a&#160;diameter of the ring. The ring now rotates with&#160;angular velocity given by:

Question 9 : A force $\vec { F } =\alpha \hat { i } +3\hat { j } +6\hat { k }$ is acting at a point $\vec { r } =2\hat { i } -6\hat { j } -12\hat { k }$. The value of $\alpha$ for which angular momentum about origine is conserved is

Question 10 : If a disc slides from top to bottom of an inclined plane, it takes time ${t}_{1}$. If it rolls, it takes time ${t}_{2}$. Now $\cfrac { { t }_{ 2 }^{ 2 } }{ { t }_{ 1 }^{ 2 } } $ is:

Question 11 : A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

Question 12 : A metal disc of radius $R$ and mass $M$ freely rolls&#160;down from the top of an inclined plane of height $h$&#160;without slipping. The speed of its centre of mass&#160;on reaching the bottom of the inclined plane is:<br/>

Question 13 : STATEMENT-1<br/>Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are&#160;simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will&#160;reach the bottom of the inclined plane first.<br/>STATEMENT-2<br/>By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach&#160;the bottom of the incline.

Question 14 : The rolling object rolls without slipping down an inclined plane (angle of inclination $\theta$), then the minimum acceleration it can have is :

Question 15 : A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first ?

Question 16 : Consider three uniform solid spheres (i) has radius '$r$' and mass '$m$', sphere (ii) radius $r$ and mass $3m$, sphere (iii) has radius $3r$ and mass $m$. All the spheres can be placed at the same point on the same inclined plane where they will roll without slipping to the bottom. If allowed to roll down the incline, then at the bottom of the incline:<br/>

Question 17 : Three bodies a ring $\left(R\right)$, a solid cylinder&#160;$\left(C\right)$ and a solid sphere&#160;$\left(S\right)$ having same mass and same radius roll down the inclined plane without slipping. They start from rest, if ${v}_{R}$, ${v}_{C}$ and ${v}_{S}$ are velocities of respective bodies on reaching the bottom of the plane, then:

Question 18 : Three bodies , a ring , a solid cylinder and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical. Which of the bodies reaches the ground with maximum velocity?

Question 19 : Assertion: A solid sphere and a hollow sphere when allowed to roll down on an inclined plane, the solid sphere reaches the bottom first. Reason: Moment of inertia of solid sphere is greater than that of hollow sphere.

Question 20 : Calculate the ratio of the times taken by a uniform solid sphere and a disc of the same mass and the same diameter to roll down through the same distance from rest on a smooth inclined plane.

Question 21 : A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. The potential at the centre of the sphere is

Question 22 : A solid sphere is rolling without slipping on a level surface at a constant speed of $2.0\ ms^{-1}$. How far can it roll up a $30^{o}$ ramp before it stops?

Question 23 : Three similar spheres of mass $m$ and radius $r$ are moving down along three inclined planes $A, B$ and $C$ of&#160;similar dimensions. Sphere on inclined plane $A$ falls freely, sphere on inclined plane $B$ rolls without slipping and sphere on inclined plane $C$ slides down then:

Question 24 : A solid cylinder is placed on the end of an inclined plane. It is found that the plane can be tipped at an angle $\theta$ before the cylinder starts to slide. When the cylinder turns on its sides and is allowed to roll, it is found that the steepest angle at which the cylinder performs pure rolling is $\phi$. The ratio $tan\phi : tan\theta$ is:

Question 25 : Two uniform solid spheres of unequal masses and unequal radii are released from rest from&#160;the same height on a rough inclined plane. The spheres roll without slipping then :

Question 26 : A cylinder rolls up an inclined plane, reaches some height and then rolls down (without slipping through these motion). The direction of the frictional force acting on cylinder are

Question 27 : A hoop of mass $m$ is projected on a floor with linear velocity ${v}_{0}$ and reverse spin ${\omega}_{0}$. The coefficient of friction between the hoop and the ground is $\mu$.<br/>Under what condition will the hoop return back?<br/>

Question 28 : A uniform solid spherical ball is rolling down a smooth inclined plane from a height $h$. The velocity attained by the ball when it reaches the bottom of the inclined plane is $v$. If the ball is now thrown vertically upwards with the same velocity $v$, the maximum height to which the ball will rise is:

Question 29 : An object of radius 'R' and mas 'M' is rolling horizontally without slipping with speed 'V'. It the rolls up the hill to a maximum height $h=3v^2{/4g}$. The moment of inertia of the object is:(g=acceleration due to gravity)<br/>

Question 30 : A wheel of radius $0.5 \ m$ rolls without sliding on a horizontal surface, starting from rest, the wheel moves with constant acceleration&#160;$\displaystyle 6\ { rad }/{ { s }^{ 2 } }$. The distance travelled by the centre of the wheel from $t=0$ to $t=3\ s$ is:

Question 31 : A solid cylinder rolls down an inclined plane. Its&#160;mass is $2 &#160;kg$ and radius $0.1 &#160;\ m$. If the height of&#160;the inclined plane is $4 &#160;m$, its rotational kinetic&#160;energy, when it reaches the foot of the plane is:<br/>

Question 32 : A and B are two solid spheres of equal masses.&#160;A rolls down an inclined plane without slipping&#160;from a height $H$. B falls vertically from the same&#160;height. Then on reaching the ground.<br/>

Question 33 : The kinetic energy $T$ of a particle moving along a&#160;circle of radius $R$ depends on the distance covered&#160;as $T=as^{2}$. The force acting on the&#160;particle is:<br/>

Question 34 : A cord is wound around the circumference of a bicycle wheel (without tyre) of diameter $1 &#160;m$. A mass of $2 &#160;kg$ is tied to the end of the cord and it is allowed to fall from rest. The weight falls $2 &#160;m$ in $4 &#160;s$. The axle of the wheel is horizontal and the wheel rotates with its plane vertical. The angular acceleration produced is:(take $g=10 &#160;ms^{-2}$)&#160;<br/>

Question 35 : 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 36 : A hoop of mass $m$ is projected on a floor with linear velocity ${v}_{0}$ and reverse spin ${\omega}_{0}$. The coefficient of friction between the hoop and the ground is $\mu$.&#160;How long will it continue to slip after its centre of mass becomes stationary?

Question 37 : A circular track has a circumference of 3140 m with AB as one of its diameter shooter moves from A to B along the circular path with a uniform speed of 10

Question 38 : A slender uniform rod of mass $M$ and length $l$ is provided at one end so that it can rotate in a vertical plane$.$ There is negligible friction at the pivot$.$ The free end is held vertically above the pivot and then released$.$ The angular acceleration of the rod when it makes an angle $\theta $ with me

Question 39 : What is the ratio of the linear speeds for the tips of hour and minute hands of a clock if the minute hand is $2.5$ times longer than the hour hand?

Question 40 : A billiard ball of mass $m$ and radius $r$, when hit in a horizontal direction by a cue at a height $h$ above its centre, acquired a linear velocity ${ v }_{ 0 }$. The angular velocity ${ \omega }_{ 0 }$ acquired by the ball is

Question 41 : A rigid body is in pure rotation, that is, undergoing fixed axis rotation. Then which of the following statement(s) are true?

Question 42 : A grinding wheel attained a velocity of $20\ rad/sec$ in $5\ sec$ starting from rest. Find the number of revolutions made by the wheel.

Question 43 : If the shaft of a flywheel has an angular speed of $120 \pi rad/s$, then the number of revolutions made by the flywheel per minute is:

Question 44 : The velocity of a car travelling on a straight road is $36 kmh^{-1}$ at an instant of time. Now travelling with uniform acceleration for 10 s, the velocity becomes exactly double. If the wheel radius of the car is 25 cm, then which of the following numbers is the closest to the number of revolutions that the wheel makes during this 10 s?

Question 45 : A particle is moving in a circle of radius $R$ in such a way that any instant the total acceleration makes an angle of ${45}^{o}$ with radius. The initial speed of the particle is ${ v }_{ 0 }$. The time taken to complete the first revolution is