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A lighter body and heavier body both are moving with same momentum and applying same retarding force. Their stoping distances are $s_1<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>s_2$ respectively. Then the correct relation between $s_1<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>s_2$.
(1) $s_1>s_2$
(2) $s_1<s_2$
(3) $s_1=s_2$
(4) None of these

A body is projected with velocity $20\sqrt{3}$ m/s with an angle of projection ${60}^0$ with horizontal. Calculate velocity on that point where body makes an angle ${30}^0$ with the horizontal.
(1) 20 m/s
(2) $\frac{20}{\sqrt{3}}m/s$
(3) $10\sqrt{3}<mspace\; width="1em"></mspace>m/s$
(4) 10 m/s

Relation between velocity (v) and time (t) is $v\alpha \sqrt{t}$, then which one of the following quantity is constant:
(1) Force
(2) Power
(3) Momentum
(4) Kinetic Energy

A particle is moving with velocity $\stackrel{\rightharpoonup }{V}=k\left(y\hat{i}<mspace\; width="1em"></mspace>+x\hat{j}\right);$ where k is constant. The general equation for path is
1. $\mathrm{y}={\mathrm{x}}^2+\mathrm{constant}$
2. ${\mathrm{y}}^2={\mathrm{x}}^2+\mathrm{constant}$
3. $\mathrm{y}=\mathrm{x}+\mathrm{constant}$
4. xy=constant

A block is kept on a rough inclined plane with angle of inclination $\theta$. The graph of net reaction (R) versus $\theta$ is.
1. 
2. 
3. 
4. None of these

A block is placed on a rough horizontal plane. A time dependent horizontal force $F=kt$ acts on the block. The acceleration time graph on the block is
1. 
2. 
3. 
4. 

A ball is thrown downwards with velocity v from the top of a tower and it reaches the ground with speed 3V What is the height of the tower?
(1) $v^2<mspace\; width="1em"></mspace>/g$
(2) $2v^2<mspace\; width="1em"></mspace>/<mspace\; width="1em"></mspace>g$
(3) $4v^2<mspace\; width="1em"></mspace>/<mspace\; width="1em"></mspace>g$
(4) $8v^2<mspace\; width="1em"></mspace>/<mspace\; width="1em"></mspace>g$

The acceleration a (in $m{s}^{-1}$) of a body, starting from rest varies with time t (in s) following the equation a=3 t+4. The velocity of the body at time t=2s will be:
(1) 10 $m{s}^{-1}$
(2) $18<mspace\; width="1em"></mspace>m{s}^{-1}$
(3) $14<mspace\; width="1em"></mspace>m{s}^{-1}$
(4) $26<mspace\; width="1em"></mspace>m{s}^{-1^{}}$
 
 

A stone falls freely from rest from a height h and it travels a distance $\frac{9h}{25}$ in the last seconds. The value of h is:
(1) 145 m
(2) 100 m
(3) 122.5 m
(4) 200 m

Given that $\overrightarrow{C}=\overrightarrow{A}+\overrightarrow{B}$ and $\overrightarrow{C}$ makes an angle $\alpha$ with $\overrightarrow{A}$ and $\beta$ with $\overrightarrow{B}$. Which of the following options is correct ?
1. $\alpha$ cannot be less than $\beta$
2. $\alpha$ < $\beta$, if A<B
3. $\alpha$ < $\beta$, if A>B
4. $\alpha$ < $\beta$, if A=B

A particle is projected with a velocity u making an angle $\mathrm{\theta }$ with the horizontal. At any instant, its velocity V is at right angles to its initial velocity u; then V is:
1. u cos $\mathrm{\theta }$
2. u tan $\mathrm{\theta }$
3. u cot $\mathrm{\theta }$
4. u sec $\mathrm{\theta }$

A projectile is given an initial velocity of $\hat{i}+2\hat{j}$. The cartesian equation of its path is (g = 10 ms^-2)
1. $\mathrm{y}=2\mathrm{x}-5{\mathrm{x}}^2$
2. $\mathrm{y}=\mathrm{x}-5{\mathrm{x}}^2$
3. $4\mathrm{y}=2\mathrm{x}-5{\mathrm{x}}^2$
4. $\mathrm{y}=2\mathrm{x}-25{\mathrm{x}}^2$

A ship A is moving westwards with a speed of 10 km h^-1 and a ship B, 100 km south of A is moving northwards with a speed of 10 km h^-1. The time after which the distance between them becomes shortest, is:
1. 5 hr
2. 5$\sqrt{2}$ hr
3. 10$\sqrt{2}$ hr
4. 0 hr

A sphere of mass m moving with constant velocity hits another sphere of same mass at rest. If e is the coefficient of restitution. The ratio of their velocities after collision is
1. 1 + e
2. $\frac{1+\mathrm{e}}{2}$
3. $\frac{1+2\mathrm{e}}{1-2\mathrm{e}}$
4. $\frac{1-\mathrm{e}}{1+\mathrm{e}}$

A rod of length L and mass M is acted on by two unequal forces F₁ and F₂(<F₁) as shown in the following figure.

The tension in the rod at a distance y from the end A is given by:
1. $F_1\left(1-\frac{y}{L}\right)+F_2\left(\frac{y}{L}\right)$
2. $F_2\left(1-\frac{y}{L}\right)+F_1\left(\frac{y}{L}\right)$
3. $\left(F_1-F_2\right)\frac{y}{L}$
4. None of the above

A river is flowing with a speed of 1 km/hr. A swimmer wants to go to point 'C' starting from 'A'. He swims with a speed of 5 km/hr, at an angle $\theta$ with respect to the river. If AB = BC = 400 m. Then -

1. time taken by the man is 12 min
2. time taken by the man is 8 min
3. the value of $\theta$ is 45^o
4. the value of $\theta$ is 53^o

Two blocks A and B of masses m & 2 m respectively are held at rest such that the spring is in natural length. Find the accelerations of both the blocks just after release.

1. $g\downarrow ,g\downarrow$
2. $\frac{g}{3}\downarrow , \frac{g}{3}\uparrow$
3. 0,0
4. $g\downarrow , 0$

In the figure shown the potential energy U of a particle is plotted against its position 'x' from origin. Then which of the following statement is correct.

1. x₁ is in stable equilibrium
2. x₂ is in stable equilibrium
3. x₃ is in stable equilibrium
4 none of these