Question 1 :
A spaceman in training is rotated in a seat at the end of a horizontal rotating arm of length $5m$. If he can withstand acceleration upto $9\dfrac{m}{s^2}$, then what is the maximum number of revolutions per second permissible?<br/>Take $g=10m/{s}^{2}$
Question 3 :
A car is moving in a circular track of radius 10 m with a constant speed of 10 m/s.A plumb bob is suspended from the roof of the car by a light weight rigid rod of 1 m long.The angle made by the rod with track is:
Question 4 :
A partial is projected vertically upwards. Its height $'h'$ and time $t'$ are related by $h = 60t - 16t^2$. The velocity at which it hits the ground is:
Question 5 :
The coordinates of a moving particle at any time $t$ are given by $ x =\alpha t^{3}$ and $y =\beta t^{3}$ . The speed of the particle at time $t$ is given by :
Question 6 :
A particle moves in a way such that its position can be expressed with $x\left( t \right) ={ t }^{ 2 }+t-3$ and with $y\left( t \right) ={ t }^{ 3 }-\dfrac { 1 }{ t-1 }$, with being time in seconds. $ x\left( t \right) $ and $y\left( t \right) $ are both in meters.<br>Initially, how far away is the particle from the origin?
Question 7 :
A body is moving along a straight line. Its distance ${ X }_{ t }$ from a point on its path at a time $t$ after passing that point is given by ${ X }_{ t }=8{ t }^{ 2 }-3{ t }^{ 3 }$, where ${ X }_{ t }$ is in meter and $t$ is in second. The correct statement(s) is/are: <br>
Question 8 :
The equation of the path of the projectile is $y=0.5x-0.04x^{2}$ The initials speed of the projectile is
Question 10 :
A particle moves along with x-axis. The position x of article with respect to time t from origin given by $x=b^0+b_1t+b_2t^2$. The acceleration of particle is:
Question 11 :
A shaft initially rotating at $1725$ rpm is brought to rest uniformly in $20s.$ The number of revolutions that the shaft will make during this time is<br><br>
Question 12 :
A particle projected at some angle with velocity $50\ m/s$, crosses a $20\ m$ high wall, after $4\ s$ from the time of projection. The angle of projection of the particle is ?
Question 13 :
If a body placed at the origin is acted upon by a force $\overline{F}=(\hat{i}+\hat{j}+\sqrt2\hat{k})$, then which of the following statements are correct?<br>1.Magnitude of $\overline{F}$ is $(2+sqrt2)$<br>2.Magnitude of $\overline {F}$ is 2<br>3. $\overline {F}$ makes an angle of $45^0$ with the Z-axis.<br>4. $\overline {F}$ makes an angle of $30^0$ with the Z-axis.<br>Select the correct answer using the codes given below.
Question 14 :
In Uniform circular motion direction of velocity is along the _______ drawn to the position of particle on the circumference of the circle. <br>
Question 15 :
While travelling from one station to another, a car travels $75\ km$ North, $60\ km$ North-east and $20\ km$ East. The minimum distance between the two stations is
Question 16 :
A man in a minivan rounds a circular turn at a constant speed.<br>Which of the following would cause the minivan to experience less acceleration?
Question 17 :
A wheel has a speed of 1200 revolutions per minute and is made to slow down at a rate of 4 rad/s$^2$. The number of revolutions it makes before coming to rest is:
Question 19 :
A point moves in xy-plane according to equation $x=at, y=at(1-bt)$ where $a$ and $b$ are positive constants and $t$ is time. The instant at which velocity vector is at $\pi /4$ with acceleration vector is given by:<br/>
Question 20 :
Assertion: In high jump, it hurts less when an athlete lands on a heap of sand.
Reason: Because of greater distance and hence greater time over which the motion of an athlete is stopped, the athlete experiences less force when lands on the heap of sand.
Question 21 :
Ship A is located $4\ km$ north and $3\ km$ east of ship B. Ship A has a velocity of $20\ kmh^{-1}$ towards the south and ship B is moving at $40 \ kmh^{-1}$ in a direction $37^o$ north of east. X and Y axes are along east and north directions, respectively.
Question 22 :
Consider the lines: <br/>$\displaystyle L_{1}:\dfrac{x+1}{3}= \dfrac{y+2}{1}= \dfrac{z+1}{2}$ and $\displaystyle L_{2}:\frac{x-2}{1}= \dfrac{y+2}{2}= \dfrac{z-3}{3}$.The unit vector perpendicular to both $\displaystyle L_{1}$ and $\displaystyle L_{2}$ is
Question 23 :
A particle moves in the $x-y$ plane according to the law $x = kt, y = kt (1 - \alpha t) $  where $k$ and $\alpha $   are positive constants and $t$ is time. The trajectory of the particle is:<br/>
Question 24 : A large number of particles are moving towards each other with velocity $V$ having directions of motion randomly distributed. What is the average relative velocity between any two particles averaged over all the pairs?<p></p>
Question 26 :
Consider a collection of large number of particles, each moving with a speed $v$. The direction of velocity is randomly distributed in the collection. The magnitude of the relative velocity between a pair of particles averaged over all the pairs in the collection :
Question 28 :
The relation between time $t$ and distance $x$ is $t = a{x^2} + bx,$ where $a$ and $b$ are constants. The acceleration is:
Question 29 :
Two particles are simultaneously projected in the same vertical plane from the same point with velocities u and v at angles $\displaystyle \alpha \:and\:\beta $ with horizontal. Find the time that elapses when their velocities are parallel.
Question 30 :
A particle of mass $m$ and charge $q$ is thrown horizontally with a velocity $v$ from top of the building of height $H$. An electric field exists in the plane and it is horizontally away from the building.<br>Which of the following is true
Question 31 :
A particle is projected at an angle of $30^{\circ}$ with respect to the horizontal with speed $20 m/s$. The angle between velocity vector and position vector at $t = 1s$ is :
Question 32 :
<br/>A particle of mass $m$ moves in a circle of radius $R$. The distance $s$ described by it varies with time $t$ as ${s}=\alpha {t}^{2}$, where $\alpha$ is a constant. What is its radial acceleration?
Question 33 :
When a man stands on a moving escalator he goes up in $40s$ and when he walked up the moving escalator he goes up in $20\ s$. The man walk up the stationary escalator in a time of:
Question 34 :
A wheel is making Revolution about axis with uniform angular acceleration, Starting from rest, it reaches $100\ rev/sec$ in $4\ seconds$. Find the angular rotated during these four seconds.
Question 35 :
A particle moves along the curve $\displaystyle y= \frac{x^{2}}{2}.$ Here $x$ varies with time as $\displaystyle x= \frac{t^{2}}{2}.$ Where $x$ and $y$ are measured in meter and $t$ in second. At $t =2\ s$, the velocity of the particle (in $\displaystyle ms^ {-1}$)  is<br/>
Question 36 :
If $\widehat{a}, \widehat{b}$ and $\widehat{c}$ are three unit vectors, such that $\widehat{a} + \widehat{b} + \widehat{c}$ is also a unit vector and $\theta_1, \theta_2$ and $\theta_3$ are angles between the vectors $\widehat{a}, \widehat{b}; \widehat{b}, \widehat{c}$ and $\widehat{c}, \widehat{a}$, respectively, then among $\theta_1, \theta_2$ and $\theta_3$
Question 37 :
Two paper screens $A$ and $B$ are separated by $150\ m$. A bullet pierces $A$ and $B$. The hole in $B$ is $15\ cm$ below the hole is $A$. If the bullet is travelling horizontally at the time of hitting $A$, then the velocity of the bullet at $A$ is $(g = 10\ ms^{-2})$.
Question 38 :
A body moves in a plane so that the displacements along the x and y axes are given by $x = 3t^3$ and $y = 4t^3$. The velocity of the body is :
Question 39 :
An object is projected with velocity $20m{s}^{-1}$ making an angle of ${45}^{o}$ with horizontal. The equation for its trajectory is $h=Ax-B{x}^{2}$ where $h$ is the height and $x$ the horizontal distance at any instant. The ratio of constants A:B is
Question 40 :
$x$ and $y$-coordinates of a particle in motion, as functions of time $t$ , are given by<br>$x = 7 t ^ { 2 } - 4 t + 6 , y = 3 t ^ { 3 } - 3 t ^ { 2 } - 12 t - 5$ ( $x \text { and } y$ are in $m$ and $t$ is in $s$.)<br>The $x \text { and } y$-components of the average velocity, in the interval from $t = 0 \text { s to } t = 5 s$ are
