Conservation of Momentum

Q.

A particle of charge q and mass m is subjected to an electric field $E=E_0\left(1-a{x}^2\right)$ in the x-direction, where $a$ and $E_0$are constants. Initially the particle was at rest at $x=0$. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is:

1. $\sqrt{\frac{2}{a}}$

2. $a$

3. $\sqrt{\frac{3}{a}}$

4. $\sqrt{\frac{1}{a}}$

Q. A 0.5 kg ball moving with a speed of $12\text{m/s}$ strikes a rigid wall at an angle of ${30}^{\circ }$ with the wall. It is reflected with the same speed at the same angle. If the ball is in contact with the wall for 0.25 second, the average force acting on the wall is

1. 48 N
2. 96 N
3. 12 N
4. 24 N

Q. A block of mass $m$ is pushed towards a movable wedge of mass $nm$ and height $h$, with a velocity $u$. All surfaces are smooth. The minimum value of $u$ for which the block reaches the top of the wedge is -

1. $\sqrt{2gh}$
2. $2ngh$
3. $\sqrt{2gh}(1-\frac{1}{n})$
4. $\sqrt{2gh(1+\frac{1}{n})}$

Q.

Two small bodies of masses 10 kg and 20 kg are kept a distance 1.0 m apart and released, assuming that only mutual gravitational forces are acting find the speeds of the particles when the separation decreases to 0.5 m.

Q.

Why does one get hurt jumping from a great height to the floor?

Q. A ball of mass $10kg$ is moving with a velocity of $10m/s$. It strikes another ball of mass $5kg$, which is moving in the same direction with a velocity of $4m/s$. If the collision is elastic, their respective velocities after the collision will be

1. $12m/s,6m/s$
2. $12m/s,25m/s$
3. $6m/s,12m/s$
4. $8m/s,20m/s$

Q. A man is standing on a cart of mass double the mass of the man. Initially cart is at rest on the smooth ground. Now man jumps with relative velocity ${}^{\prime }{v}^{\prime }$ horizontally towards right with respect to cart. Find the work done by man during the process of jumping.

1. $\frac{m{v}^2}{3}$
2. $m{v}^2$
3. $\frac{m{v}^2}{6}$
4. none of the above

Q. The kinetic energy of an electron which is accelerated through a potential of 100 volts is

1. $6.626\times {10}^{-34}W-sec$
   

2. $1.602\times {10}^{-17}J$

3. 418.6 calories

4. $1.16\times {10}^{4}J$

Q. The isotope ${}_5^{12}B$ having a mass 12.014 u undergoes $\beta$ -decay to ${}_6^{12}C$ , ${}_6^{12}C$ has an excited state of the nucleus (${}_5^{12}{C}^{\ast }$ ) at $4.041MeV$ above its ground state. If ${}_5^{12}B$ decays to ${}_6^{12}{C}^{\ast }$, the maximum kinetic energy of the $\beta$-particle in units of $MeV$ is
($1u=931.5MeV/c^2$, where c is the speed of light in vacuum).

Q. A man has $80\text{kg-wt}$ on the surface of Earth of radius $\left(R\right)$. At what height above the surface of the Earth his weight will be $40\text{kg-wt}$ ?

1. $\frac{R}{2}$
   
2. $\sqrt{2}R$
3. $(\sqrt{2}-1)R$
4. $(\sqrt{2}+1)R$

Q.

Name the factors on which momentum depends on.

Q. A ball of mass 50g is dropped from a height of 20m.a boy on the ground hits the ball vertically upwards with a bat with an average force of 200N;so that it attains vertical height of 45m.what is the time for which the ball remains in contact with the bat?

Q.

The moment of momentum is known as __________

Q.

Two particles having masses $4g$ and $16g$ respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is$n:2$. The value of $n$ will be_____.

Q. In the given figure , two wheels $P$ and $q$ are connected by a belt $B$. The radius of $P$ is three times as that of $Q$. In case of same rotational kinetic energy, the ratio of rotational inertias $\left(\frac{I_P}{I_Q}\right)$ will be $x:1$. The value of $x$ will be

Q.

A wagon weighing 1000 kg is moving with a velocity 50 km/h on smooth horizontal rails. A mass of 250 kg is dropped into it. The velocity with which it moves now is

1. 20 km/hour

2. 12.5 km/hour

3. 40 km/hour

4. 50 km/hour

Q.

Qualitative definition of force is given by

1. Newtons first law of motion

2. Newtons second law of motion

3. Newtons third law of motion

4. Newtons law of gravitation

Q. A ball moves over a fixed track as shown in figure. From $A$ to $B$, the ball rolls without slipping. Surface $BC$ is frictionless. $K_A,K_B$ and $K_C$ are kinetic energies of the ball at $A$, $B$ and $C$ respectively. Then choose the correct alternative below-

$\left(a\right)h_A>h_C;K_B>K_C\left(b\right)h_A>h_C;K_C>K_A\left(c\right)h_A=h_C;K_B=K_C\left(d\right)h_A<h_C;K_B>K_C$

1. $a,b$
2. $a,c$
3. $b,d$
4. $Noneofthese$

Q.

Two friends on roller skates are standing $5m$ apart facing each other. One of them throws a ball of $2Kg$ towards the other, who catches it, How will this activity affect the position of the two? Explain your answer.

Q. A bomb of mass $3m\text{kg}$ explodes into two pieces of mass $m\text{kg}$ and $2m\text{kg}$ . If the velocity of $m\text{kg}$ mass is $16\text{m/s}$, the total energy released in the explosion is

1. $192m\text{J}$
2. $96m\text{J}$
3. $768m\text{J}$
4. $384m\text{J}$

Q. A bullet of mass $50\text{gm}$ is fired from below onto a bob of mass $450\text{gm}$ of a long simple pendulum as shown in the figure. The bullet remains inside the bob and the bob rises through a height of $1.8\text{m}$ vertically upwards. Find the speed of the bullet.

1. $60\text{m/s}$
2. $80\text{m/s}$
3. $40\text{m/s}$
4. $20\text{m/s}$

Q. A particle of mass $m$ is placed on top of a smooth hemispherical wedge of mass $4m$ at rest. The hemispherical wedge is kept on a frictionless horizontal surface. The particle is given a gentle push. The angular velocity of the particle relative to the wedge, if wedge has velocity $v$ when particle has falls by an angle $\theta$ with respect to the wedge is

1. $\frac{5v}{R\cos \theta }$
2. $\frac{5v}{2R\cos \theta }$
3. $\frac{4v}{R\cos \theta }$
4. $\frac{5v}{R\sin \theta }$

Q.

Name the factor on which the momentum of a body depends.

Q. Initially a man and a plank of the same mass $m$ are moving on smooth horizontal surface with a velocity $v\text{m/s}$ along positive x-axis. After some time man jumps along negative x-axis with a velocity $v\text{m/s}$ with respect to ground, then the speed of the plank will be

1. $3v\text{m/s}$
2. $v\text{m/s}$
3. $2v\text{m/s}$
4. $\text{None of these}$

Q. A particle A suffers an oblique elastic collision with a particle B that is at rest initially. If their masses are the same, then, after the collision

1. They will move in the opposite direction
2. A comes to rest and B starts moving in the direction of the original motion of A
3. A continues move in the original direction while B remains at rest
4. They will move in the mutually perpendicular directions

Q. A gun fires a shell and recoils horizontally. if the shell travels along the barrel with speed $v$, the ratio of speeds with which the gun recoils, if the barrel is (i) horizontal (ii) inclined at an angle of ${30}^{\circ }$ with horizontal, is

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

Q. The potential energy of a system of two particles is given by $U\left(x\right)=\frac{a}{x^2}-\frac{b}{x}$ . Find the minimum potential energy of the system, where $x$ is the distance of separation and $a,b$ are positive constants.

1. $-\frac{b^2}{4a}$
2. $\frac{b}{2}[\frac{a^2}{b^2}-1]$
3. $\frac{a}{3}[\frac{a^2}{b^2}-1]$
4. $-\frac{a^2}{4b}$

Q. A ball is dropped from a height $h$ above a point on an inclined plane with an angle of inclination $\theta$. The ball makes an elastic collision with the surface and rebounds off the plane. Determine the distance from the point of first impact to the point where ball hits the plane second time.

1. $2h\sin \theta$
2. $4h\sin \theta$
3. $2h\cos \theta$
4. $8h\sin \theta$

Q.

A geostationary satellite is revolving around the earth. To make it escape from gravitational field of earth, its velocity must be increased

1. $100\%$

2. $41.4\%$

3. $50\%$

4. $59.6\%$

Q. A particle of mass $m_1$ moves with speed $u_1$ and collide head on with a stationary particle of mass $m_2$. After the collision, the velocities of the particles are $v_1$ and $v_2$, and $e$ is coefficient of restitution for the collision. If $v_1$ is to be positive, i.e., for the first particle to continue moving in same direction then:

1. $\frac{m_2}{m_1}>e$
2. $\frac{m_1}{m_2}>e$
3. $\frac{m_1+m_2}{m_2}>e$
4. $\frac{m_1-m_2}{m_2}>e$