Examples

Q.

Initial fuel in a rocket is $1000kg.$ If it was given an acceleration of $20\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$ the velocity of fuel with respect to the rocket is $500\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$. Find the rate of consumption of fuel.

1. $30\raisebox{1ex}{$kg$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

2. $60\raisebox{1ex}{$kg$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

3. $900\raisebox{1ex}{$kg$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

4. $80\raisebox{1ex}{$kg$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Q.

What is the relation between drift velocity and electric field?

Q. A particle of mass $m$ is attached to one end of a mass-less spring of force constant $k,$ lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time $t=0$ with an initial velocity $u_0$. When the speed of the particle is $0.5u_0,$ it collides elastically with a rigid wall. After this collision

1. The time at which the maximum compression of the spring occurs is $t=\frac{4\pi }{3}\sqrt{\frac{m}{k}}$
2. The speed of the particle when it returns to its equilibrium position is $u_0$
3. The time at which the particle passes through the equilibrium position for the second time is $t=\frac{5\pi }{3}\sqrt{\frac{m}{k}}$
4. The time at which the particle passes through the equilibrium position for the first time is $t=\pi \sqrt{\frac{m}{k}}$

Q. The initial mass of a rocket is $1000\text{kg}$. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of $20{\text{ms}}^{-2}$. the gases come out at a relative speed of $500{\text{ms}}^{-1}$ with respect to the rocket : [use $g=10{\text{ms}}^{-2}$]

1. $60{\text{kg s}}^{-1}$
2. $6.0\times {10}^2{\text{kg s}}^{-1}$
3. $500{\text{kg s}}^{-1}$
4. $10{\text{kg s}}^{-1}$

Q. A wire has a non-uniform cross-section, as shown in the figure. A steady current flows through it. The drift speed of electrons at points $P$ and $Q$ are $v_P$ and $v_Q$ respectively, then -

1. $v_P=v_Q$
2. $v_P<v_Q$
3. $v_P>v_Q$
4. Data insufficient

Q.

A light and a heavy object have the same momentum. Find out the ratio of their kinetic energies. Which one has a larger kinetic energy?

Q. Two bodies $A$ and $B$ of masses $m$ and $2m$ respectively placed on a smooth floor are connected by a spring. A third body $C$ of mass $m$ moves with velocity $v_0$ along the line joining $A$ and $B$ and collides elastically with $A$. At a certain instant of time $t_0$ after collision it is found that the instantaneous velocities of $A$ and $B$ are same. The compression in the spring at $t_0$ is $x_0$, then:

1. The common velocity of $A$ and $B$ at time $t_0$ is $\frac{v_0}{3}$.
2. The spring constant is $k=\frac{3m{v}_0^2}{2x_0^2}$.
3. The spring constant is $k=\frac{2m{v}_0^2}{3x_0^2}$ .
4. None

Q. A spring is compressed between two blocks of masses $m_1$ and $m_2$ placed on a horizontal frictionless surface as shown in the figure. When the blocks are released, they have initial velocity of $v_1$ and $v_2$ as shown. The blocks travel distances $x_1$ and $x_2$ respectively before coming to rest.
The ratio $\left(\frac{x_1}{x_2}\right)$ is

1. $\frac{m_2}{m_1}$
2. $\frac{m_1}{m_2}$
3. $\sqrt{\frac{m_2}{m_1}}$
4. $\sqrt{\frac{m_1}{m_2}}$

Q.

Find the area bounded by the curve y = $e^{-x}$, the X -axis and the Y-axis.

Q. The area of cross section of a current carrying conductor is $A_0$ and $\frac{A_0}{4}$ at section $\left(1\right)$ and $\left(2\right)$ respectively. If $v_1$ and $v_2$ are the drift velocity of region $\left(1\right)$ and $\left(2\right)$ respectively then

1. $v_1:v_2=1:4$
2. $v_1:v_2=2:1$
3. $v_1:v_2=3:2$
4. $v_1:v_2=1:3$

Q. A cart of mass $50\text{kg}$ is moving on a straight track with a speed of $12\text{m/s}$. A mass of $10\text{kg}$ is gently put into the cart. What will be the velocity of the cart after this?

1. $12\text{m/s}$
2. $10\text{m/s}$
3. $14\text{m/s}$
4. $16\text{m/s}$

Q. A ball is moving with velocity $2\text{m/s}$ towards a heavy wall approaching the ball with a speed $1\text{m/s}$ as shown in figure. Assuming collision to be elastic, find the velocity of the ball immediately after the collision.
(Considering the initial direction of motion of ball to be $+ve$).

1. $-2\text{m/s}$
2. $-4\text{m/s}$
3. $1\text{m/s}$
4. $-3\text{m/s}$

Q.

The momentum p of a particle changes with time t according to the relation $\frac{dp}{dt}$ = (10 N) + $\left(2\frac{N}{s}\right)$t. If the momentum is zero at t= 0, what will the momentum be at t = 10 s?

Q. Find the integration of $\int \frac{e^{{\sin }^{-1}x}}{\sqrt{1-x^2}}.dx$

1. $e^{{\sin }^{-1}x}+C$
2. $e^{-{\sin }^{-1}x}+C$
3. $\frac{e^{{\sin }^{-1}x}}{2}+C$
4. $e^{\sin x}+C$

Q.

A moving body of mass $10kg$ has $20J$ of kinetic energy. Calculate its speed.

Q.

A block of mass 2.0 kg is moving on a friction less horizontal surface with a velocity of 1.0 m/s below figure towards another block of equal mass kept at rest.The spring constant of the spring fixed at one end is 100 N/m.Find the maximum compression of the spring.

Q. $O{O}^{{}^{\prime }}$ and $A{A}^{{}^{\prime }}$ are two vertical walls. A particle is projected from $O$ with speed $10m/s$ at an angle ${15}^0$ from the horizontal. All collisions with each walls are perfectly elastic. Then choose the correct statement(s).

1. The horizontal component of velocity will change after each collision.
2. Particle will land on the ground between points $O$ and $A$.
3. The total number of collisions with walls is $9$ till particle reaches ground again for the first time after projection.
4. Time taken by particle to reach the ground is $2\sin {15}^{\circ }$ seconds.

Q. A ball is moving with speed $12\text{m/s}$ towards a heavy wall which is moving towards the ball with the speed $10\text{m/s}$ as shown in figure. Assuming collision to be perfectly elastic, find the speed of ball after the collision.

1. $2\text{m/s}$
2. $32\text{m/s}$
3. $14\text{m/s}$
4. $22\text{m/s}$

Q. A rocket which is ejecting gas with a speed of $100\text{m/s}$ and the rate of ejection of the gas from the rocket is $800\text{kg/s}$. If the mass of the rocket is $4000\text{kg}$, find out the initial acceleration of the rocket. Take $(g=10{\text{m/s}}^2)$

1. $8{\text{m/s}}^2$
2. $6{\text{m/s}}^2$
3. $12{\text{m/s}}^2$
4. $10{\text{m/s}}^2$

Q. The ball of mass $m$ approaches a wall of mass $M$ with speed $6\text{m/s}$, perpendicular to the wall. The speed of the wall is $3\text{m/s}$ towards the ball. What will be the speed of the ball after collision with the wall, considering the collision to be perfectly elastic? (Assume $M>>>m$)

1. $6\text{m/s}$ away from the wall
2. $3\text{m/s}$ away from wall
3. $9\text{m/s}$ away from the wall
4. $12\text{m/s}$ away from the wall

Q. A ball of mass $m_1=4\text{g}$ thrown towards a wall with a velocity $u_1=4\text{m/s}$ collides against the wall elastically as shown in figure. What will the velocity of the ball after collision?

1. $2\text{m∕s opposite to the original direction}$

2. $4\text{m∕s opposite to the original direction}$
3. $8\text{m∕s opposite to the original direction}$
4. $6\text{m∕s opposite to the original direction}$

Q. Current is flowing through a conductor of non-uniform cross-section. If $A_1>A_2$, then the relation between the drift velocity $\left(V\right)$ and current at the two cross- sections respectively, will be

1. $V_1>V_2$ and $i_1>i_2$
2. $V_1<V_2$ and $i_1=i_2$
3. $V_1<V_2$ and $i_1<i_2$
4. $V_1=V_2$ and $i_1=i_2$

Q. A body of mass m moving with velocity $v$ collides head on with another body of mass $2m$ which is initially at rest. The ratio of $K.E.$ of colliding body before and after collision will be :$[e=1]$

1. $1:1$
2. $4:1$
3. $2:1$
4. $9:1$

Q. In a typical Indian Bugghi (a luxury cart drawn by horses), a wooden plate is fixed on the rear on which one person can sit. A bugghi of mass 200kg is moving at a spped of 10km/h. As it overtakes a school boy walking at a speed of 4 km/h, the boy sits on the wooden plate. If the mass of the boy is 25kg, what will be the new velocity of the bugghi?

1. 6 km/hr
2. 9.33 km/hr
3. 12.63 km/hr
4. none ot these

Q.

A small metal bearing of mass $m_1=30\text{g}$, moving with a velocity of $v_1=25\text{m/s}$ collides elastically with a huge sphere of mass $200\text{kg}$ moving with a velocity of $3\text{m/s}$. What is the velocity of the small metal bearing after colliision?

1. $9\text{m∕s in original direction}$
2. $19\text{m∕s opposite to the original direction}$
3. $9\text{m∕s opposite to the original direction}$
4. $19\text{m∕s in original direction}$

Q. The barrel of a gun and the target are at the same height. As soon as the gun is fired, the target is also released. In which of the following cases, the bullet will not strike the target

1. Range of projectile is less than the initial distance between the gun and the target
2. Range of projectile is more than the initial distance between the gun and the target
3. Range of projectile is equal to the initial distance between the gun and target
4. Bullet will always strike the target

Q. A ball is thrown horizontally at a heavy wall with a velocity of $15\text{m/s}$. The wall is moving in the same direction as the ball with a velocity of $8\text{m/s}$. Assuming that the collision is elastic, what is the velocity of the ball after the collision?

1. $1\text{m/s}$
2. $2\text{m/s}$
3. $7\text{m/s}$
4. $8\text{m/s}$

Q. A body of mass 'M' moving with a speed of 'u' has a head-on collision with a body of mass 'm' originally at rest. If M >> m, then the speed of the body of mass 'm' after the collision, will be nearly

1. 
2. 
3. 
4. 

Q.

A shell is fired from a cannon with a speed $100m{s}^{-1}$ at an angle $60°$with the horizontal (positive $x$-direction). At the highest point of its trajectory, the shell explodes into two equal fragments. One of the pieces moves along $x$-direction with a speed of $50m{s}^{-1}$Determine the speed of the other piece at the time of explosion.

Q. A metallic ball of mass $20\text{kg}$ moving with a velocity of $5\text{m/s}$ collides with a small plastic ball of mass $5\text{g}$ initially at rest. What is the final velocity of the plastic ball?

1. $10\text{m/s}$
2. $5\text{m/s}$
3. $0\text{m/s}$
4. $15\text{m/s}$