Q. Two projectiles are thrown with the same initial velocity at angles $\alpha$ and $({90}^{\circ }-\alpha )$ with the horizontal. The maximum heights attained by them are $h_1$ and $h_2$ respectively. Then $\frac{h_1}{h_2}$ is equal to

1. ${\sin }^2\alpha$
2. ${\cos }^2\alpha$
3. ${\tan }^2\alpha$
4. $1$

Q. A particle strikes a horizontal frictionless floor with a speed $u$ at an angle $\theta$ with the vertical, and rebounds with a speed $v$ at an angle $\varphi$ with vertical. The coefficient of restitution between the particle and floor is $e$. The magnitude of $v$ is

1. $eu$
2. $(1-e)u$
3. $u\sqrt{e^2{\sin }^2\theta +{\cos }^2\theta }$
4. $u\sqrt{{\sin }^2\theta +e^2{\cos }^2\theta }$

Q. What is the stress caused in a body? (Young's Modulus $Y$( when its length is doubled?

1. $Y$
2. $\frac{Y}{2}$
3. $2Y$
4. $\sqrt{Y}$

Q. Moment of inertial of a disc about is own axis is $I$. Its moment of inertia about a tangential axis in its plane is

1. $\frac{3}{2}I$
2. $2I$
3. $\frac{5}{2}I$
4. $3I$

Q. If $W_1,W_2$ and $W_3$ represent the work done in moving a particle from $A$ to $B$ along three different paths $1,2$ and $3$ respectively (as shown) in a gravitational field of point mass $m$, then find the correct relation between $W_1,W_2$ and $W_3$.

1. $W_1<W_2<W_3$
2. $W_2>W_1>W_3$
3. $W_1>W_2>W_3$
4. $W_1=W_2=W_3$

Q. A liquid will NOT wet the surface of a solid if its angle of contact is

1. Zero
2. Less than ${90}^{\circ }$
3. More than ${90}^{\circ }$
4. ${90}^{\circ }$

Q. A projectile $A$ is thrown at an angle of ${30}^{\circ }$ to the horizontal from point $P$. At the same time, another projectile $B$ is thrown with velocity $v_2$ upwards from the point $Q$ vertically below the highest point. For $B$ to collide with $A,\frac{v_2}{v_1}$ should be

1. $1$
2. $2$
3. $\frac{1}{2}$
4. $4$

Q. A block of mass $m$ on a rough horizontal surface is acted upon by two forces as shown in figure. For equilibrium of block, the coefficient of friction between block and surface is

1. $\frac{F_1\cos \theta +F_2}{mg+F_2\sin \theta }$
2. $\frac{F_1+F_2\cos \theta }{mg+F_2\cos \theta }$
3. $\frac{F_1+F_2\cos \theta }{mg+F_2\sin \theta }$
4. $\frac{F_1+F_2\sin \theta }{mg+F_2\cos \theta }$

Q. The time period $T$ of a small drop of liquid (due to surface tension) depends on density $\rho$, radius $r$ and surface tension $S$. The relation is

1. $T\propto \rho rS$
2. $T\propto (\rho r^3/S{)}^{1/2}$
3. $T\propto S/\rho r$
4. $T\propto \rho r/S$

Q. Which of the following quantities can be written in $SI$ units in $kg{m}^2{A}^{-2}{s}^{-3}$?

1. Resistance
2. Inductance
3. Capacitance
4. Magnetic flux

Q. As shown in the figure, water squirts horizontally out of two small holes in the side of the cylinder and the two streams strike the ground at the same point. If the hole $Q$ is at a height $h$ above the ground and the level of water stands at height $H$ above the ground, then the height of $P$ above ground level is

1. $2h$
2. $H-h$
3. $H/h$
4. $H/2$

Q. In the relation $y=r\sin (\omega t+kx)$, the dimensional formula for $kx$ or $\omega t$ is same as

1. $\omega t/r$
2. $yr/\omega t$
3. $r/\omega$
4. $r/y$

Q. A shell at rest explodes. The centre of mass of the fragments.

1. Moves along a parabolic path
2. Moves along a straight line
3. Moves along an elliptical path
4. Remains at rest

Q. The work done in stretching a spring of force constant $k$ from length $l_1$ to $l_2$ is

1. $k(l_2-l_1)$
2. $k/2(l_2-l_1)$
3. $k(l_2^2-l_1^2)$
4. $\frac{1}{2}k(l_2^2-l_1^2)$

Q. In elastic collision.

1. Both momentum and kinetic energy are conserved
2. Both momentum and kinetic energy are not conserved
3. Only energy is conserved
4. Only momentum is conserved

Q. In an experiment, on the measurement of $g$, using a simple pendulum, the time period was measured with an accuracy of $0.2$% while the length was measured with an accuracy of $0.5$%. The percentage accuracy in the value of $g$ thus obtained is

1. $0.1$%
2. $0.9$%
3. $0.7$%
4. $0.25$%

Q. In the given figure, the pulleys and the string are light. $T$ is the tension in the string. Taking $g=10m{s}^{-2}$, which of the following is correct?

1. The acceleration of the system is $10m{s}^{-2}$
2. The acceleration of the system is $5m{s}^{-2}$
3. $T=0N$
4. $T=15N$

Q. According to Bernoulli's equation $\underset{\left(A\right)}{\frac{P}{\rho g}}+\underset{\left(B\right)}{h}+\underset{\left(C\right)}{\frac{1}{2}\frac{v^2}{g}}=constant$
The terms $A,B$ and $C$ generally called respectively.

1. Gravitational head, pressure head and velocity head
2. Gravity, gravitational head and velocity head
3. Pressure head, gravitational head and velocity head
4. Gravity, pressure and velocity head

Q. A particle is moving in a circle of radius $r$ with constant speed $v$. The change in velocity in moving from $P$ to $Q$ is

1. $2v\cos {20}^{\circ }$
2. $2v\sin {20}^{\circ }$
3. $2v\cos {40}^{\circ }$
4. $2v\sin {40}^{\circ }$

Q. The change in the value of $g$ at a height $h$ about the surface of the earth is the same as at a depth $d$ below the surface of earth. When both $d$ and $h$ are much smaller than the radius of earth, then which one of the following is correct?

1. $d=\frac{3h}{2}$
2. $d=h$
3. $d=2h$
4. $d=\frac{h}{2}$

Q. Which of the following statements about angular momentum is correct?

1. It is moment of inertia
2. It is directly proportional to moment of inertia
3. It is a scalar quantity
4. All of these

Q. A ball thrown upward from the top of a tower with speed $v$ reaches the ground in $t_1$ second. If this ball is thrown downward from the top of the same tower with speed $v$ it reaches the ground in $t_2$ second. In what time the ball shall reach the ground if it is allowed to fall freely under gravity from the top of the tower?

1. $\frac{t_1+t_2}{2}$
2. $\frac{t_1-t_2}{2}$
3. $\sqrt{t_1{t}_2}$
4. $t_1+t_2$

Q. Two identical solid copper spheres of radius $R$ are placed in contact with each other. The gravitational attraction between them is proportional to

1. $R^2$
2. $R^{-4}$
3. $R^{-2}$
4. $R^4$

Q. The driver of a train travelling at $115km{h}^{-1}$ seen on the same track, $100m$ in front of him, a slow train travelling in the same direction at $25km{h}^{-1}$. The least retardation that must be applied to faster train to avoid a collision is

1. $25m{s}^{-2}$
2. $75m{s}^{-2}$
3. $50m{s}^{-2}$
4. $3.125m{s}^{-2}$

Q. Energy required to move a body of mass $m$ from an orbit of radius $2R$ to $3R$ is (where $M=$ mass of earth, $R=$ radius of earth)

1. $\frac{GMm}{12R^2}$
2. $\frac{GMm}{3R^2}$
3. $\frac{GMm}{8R}$
4. $\frac{GMm}{6R}$

Q. The root mean square velocity, $v_{rms}$, the average velocity $v_{av}$ and the most probable velocity, $v_{mp}$ of the molecules of the gas are in the order.

1. $v_{mp}>v_{av}>v_{rms}$
2. $v_{rms}>v_{av}>v_{mp}$
3. $v_{av}>v_{mp}>v_{rms}$
4. $v_{mp}>v_{rms}>v_{av}$

Q. Three particles $A,B$ and $C$ of equal mass $m$, move with equal speed $v$ along the medians of an equilateral triangle as shown in the figure. They collide at the centroid $G$ of the triangle. After collision, $A$ comes to rest and $B$ retraces its path with speed $v$. What is the speed of $C$ after collision?

1. $0$
2. $\frac{v}{2}$
3. $v$
4. $2v$

Q. What is the angle between $(\overrightarrow{A}-\overrightarrow{B})$ and $(\overrightarrow{A}\times \overrightarrow{B})$?

1. $0^{\circ }$
2. $\frac{\pi }{2}radian$
3. $\pi radian$
4. $\frac{3\pi }{2}radian$

Q. Two soap bubbles $A$ and $B$ are formed at the two open ends of a tube. The bubble $A$ is smaller than bubble $B$. If valve $V$ is opened and air can flow freely between the bubbles, then

1. There is no change in the size of the bubbles
2. The two bubbles will become of equal size
3. $A$ will become smaller and $B$ will become larger
4. $B$ will become smaller and $A$ will become larger

Q. The gas in a vessel in subjected to a pressure of $20$ atmosphere at a temperature ${27}^{\circ }C$. The pressure of the gas in the vessel after one half of the gas is released from the vessel and the temperature of the remainder is raised by ${50}^{\circ }C$, is

1. $8.5atm$
2. $10.8atm$
3. $11.7atm$
4. $17atm$