The 'e' Equation

Q.

A bullet of mass $10g$ traveling horizontally with a velocity of $150m/s$ strikes a stationary wooden block and comes to rest in $0.03s$. Calculate the distance of penetration of the bullet into the block. Also, calculate the magnitude of the force exerted by the wooden block on the bullet.

Q.

An object of mass $m_1$ collides with another object of mass $m_2$, which is at rest. After the collision, the objects move at equal speeds in opposite directions. The ratio of the masses$m_2:m_1$is:

1. $2:1$

2. $1:1$

3. $1:2$

4. $3:1$

Q. A ball moving with velocity $2{\text{ms}}^{-1}$ collides head-on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$, then their velocities (in ${\text{ms}}^{-1}$) after collision will be

1. $1,1$
2. $1,0.5$
3. $0,1$
4. $0,2$

Q. The relation 3t=$\sqrt{3x}$+6 describes the displacement of a particle in one direction where x is in metres and t in sec. The displacement, when velocity is zero, is

1. Zero
2. 12 metres
3. 5 metres
4. 24 metres

Q. A sphere of radius 1cm has potential of 8000V , then energy density near it's surface will be
a) 6400000J/m3
b) 8000J/m3
c) 32J/m3
d) 2.83J/m3

Q. A hollow sphere is filled with water through a small hole in it. It is then hung by a long thread and made to oscillate. As the water slowly flows out of the hole at the bottom, the period of oscillation will

1. First decrease and then increase to original value
2. Continuously decrease
3. Continuously increase
4. First increase and then decrease to original value

Q.

A sphere of mass $m$ moving with a constant velocity $u$ hits another stationary sphere of same mass. If $e$ is the coefficient of restitution, then ratio of velocities of the two spheres $\frac{v_1}{v_2}$ after collision will be

1. $\frac{1-e}{1+e}$
2. $\frac{e+1}{e-1}$
3. $\frac{1+e}{1-e}$
4. $\frac{e-1}{e+1}$

Q. A Ball is dropped vertically from rest at a height of 12m. After striking the ground it bounces of 9m . What fraction of its kinetic energy does it loose on striking the ground?

Q.

A body is travelling with uniform acceleration and travels $84m$ in the first $6seconds$ and $180m$ in the next $5seconds$. Find the initial velocity and acceleration of the body.

Q.

The coefficient of restitution e for a perfectly elastic collision is

1. 1

2. 0

3. 

4. - 1

Q.

A ball is dropped from a height of $10m$. If the energy of the ball reduces by $40\%$ after striking the ground, how high can the ball bounce back? ($g=10m{s}^{-2}$) .

Q.

A particle falls from a height h on a fixed horizontal plate and rebounds. If e is the coefficient of restitution, the total distance travelled by the particle before it stops rebounding is

1. $\frac{h(1-e^2)}{2(1+e^2)}$

2. $\frac{h(1+e^2)}{2(1-e^2)}$

3. $\frac{h(1+e^2)}{(1-e^2)}$

4. $\frac{h(1-e^2)}{(1+e^2)}$

Q.

A metal ball falls from a height of 32 m on a steel plate. If the coefficient of restitution is 0.5, to what height will the ball rise after the second bounce

1. 2 m

2. 4 m

3. 8 m

4. 16 m

Q.

If for $\mathrm{a}>0$, the feet of perpendiculars from the point $\mathrm{A}(\mathrm{a},-2\mathrm{a},3)$ and $\mathrm{B}(0,4,5)$ on the plane $\mathrm{lx}+\mathrm{my}+\mathrm{nz}=0$ are points $\mathrm{C}(0,-\mathrm{a},-1)$ and $\mathrm{D}$ respectively, then the length of line segment $\mathrm{CD}$ is equal to:

1. $\sqrt{41}$

2. $\sqrt{55}$

3. $\sqrt{31}$

4. $\sqrt{66}$

Q. What are the factors on which centre of mass of a body depends

Q.

If the momentum of a body is increased by 100 %, then the percentage increase in the kinetic energy is

1. 150 %

2. 200 %

3. 225 %

4. 300 %

Q.

What will be the kinetic energy of a body when its mass is made four times and the velocity is doubled?

Q.

$\mathrm{s}=3{\mathrm{t}}^2–8\mathrm{t}+5$ is the distance reached by a body in $\mathrm{t}$ seconds, and the body will stop after

1. 1 sec

2. 3 / 4 seconds

3. 4 / 3 seconds

4. 4 sec

Q. A particle of mass $3\text{kg}$ moving with a velocity of $6\hat{i}\text{m/s}$ collides head on with another particle of mass $5\text{kg}$ moving with a velocity of $-2\hat{i}\text{m/s}$. If after the collision, first particle has a speed of $1\text{m/s}$ along the negative $X$ axis, find the coefficient of restitution.

1. $0.4$
2. $0.5$
3. $0.6$
4. $0.3$

Q.

A ball collides directly with another ball at rest and is itself brought to rest by the impact. If one fourth of initial kinetic energy is destroyed in the collision, the coefficient of restitution of the collision is

1. 

2. 

3. 

4. 

Q. Two balls of mass $3\text{kg}$ and $6\text{kg}$ are moving towards each other with velocities $6\text{m/s}$ and $3\text{m/s}$ respectively on a frictionless surface. After colliding, the $3\text{kg}$ ball returns with velocity $3\text{m/s}$. Velocity of $6\text{kg}$ ball (after collision) and coefficient of restitution are respectively:

1. $1.5\text{m/s},0.5$
2. $2\text{m/s},0.20$
3. $3\text{m/s},1$
4. $2.2\text{m/s},0.3$

Q. Consider the spring-mass system, with the mass submerged in water as shown in the figure. If mass is released with spring at natural length, then momentum-position diagram for one cycle of this system is (take down direction negative) (given density of mass is more than density of water).

1. 
2. 
3. 
4. 

Q. Two billiard balls undergo a head-on collision. Ball $1$ is twice as heavy as ball $2$. Initially, ball $1$ moves with a speed $u$ towards ball $2$ which is at rest. Immediately after the collision, ball $1$ travels at a speed of $\frac{u}{3}$ in the same direction. What type of collision has occurred?

1. Inelastic
2. Elastic
3. cannot be determined from the information
4. Completely inelastic

Q.

Two identical spheres A and B lie on a smooth horizontal circular groove at opposite ends of a diameter. At time t = 0, A is projected along the groove and at time t = T, it impinges on sphere B. If e is the coefficient of restitution, the second impact will occur after a time equal to

1. $T$

2. $eT$

3. $\frac{2T}{e}$

4. $2eT$

Q.

Two fat astronauts each of mass 120 kg are travelling in a closed spaceship moving at a speed of 15 km/s in the outer space far removed from all other material objects.The total mass of the spaceship and its contents including the astronauts is 660 kg.If the astronauts do slimming exercise and thereby reduce their masses to 90 kg each, with what velocity will the spaceship move?

Q. A particle loses $25\%$ of its kinetic energy during head on collision with another identical particle initially at rest. The coefficient of restitution will be

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

Q.

When a body falls freely towards the earth, then its total energy

1. increases

2. decreases

3. remains constant

4. first increases and then decreases

Q. A block of mass $m$ moving at a velocity $v$ collides with another block of mass $2m$ at rest. The lighter block comes to rest after collision. Find the coefficient of restitution.

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

Q. A $4\text{kg}$ ball moving to the right at $6\text{m/s}$ collides with a $5\text{kg}$ ball ahead of it and moving to the right at speed $2\text{m/s}$ . Find the magnitude of final velocity of the $4\text{kg}$ and $5\text{kg}$ balls respectively, if coefficient of restitution is $0.5$.

1. $4.4\text{m/s},3.4\text{m/s}$
2. $2.66\text{m/s},4.66\text{m/s}$
3. $5\text{m/s},7\text{m/s}$
4. $3.33\text{m/s},5.33\text{m/s}$

Q. A short electric dipole is oriented along $+vex$ - direction at origin. At which of following point the electric field have no $x$ component ?

1. $(1,1,0)$
2. $(\sqrt{2},1,0)$
3. $(1,\sqrt{2},0)$
4. $(1,0,0)$