Speed of Bullet Example

Q. The velocity of a projectile at the initial point $\text{A}$ is $(2\hat{i}+3\hat{j}){\text{ms}}^{-1}.$ It's velocity (in ${\text{ms}}^{-1}$) at point $\text{B}$ is -

1. $2\hat{i}+3\hat{j}$
2. $-2\hat{i}-3\hat{j}$
3. $-2\hat{i}+3\hat{j}$
4. $2\hat{i}-3\hat{j}$

Q. A bomb bursts into three fragments , in which two fragments of equal masses of $1\text{kg}$ each are moving with speed $v$ at right angles to each other , while third fragment has mass twice that of either masses. If kinetic energy of system $($all masses$)$ increases by $96\text{J}$ after bursting then find out the correct statement about third fragement:

1. Will move with speed $4\text{m/s}$ at angle of ${135}^{\circ }$ to either
2. Will move with speed $4\sqrt{2}\text{m/s}$ at angle of ${135}^{\circ }$ to either
3. Will move with speed $4\sqrt{2}\text{m/s}$ at angle of ${45}^{\circ }$ to either
4. Will move with speed $4\text{m/s}$ at angle of ${45}^{\circ }$ to either

Q. A bullet of \(10~g\), moving with velocity \(\upsilon , \) collides head-on with the stationary bob of a pendulum and recoils with velocity \(100~\text{m/s}.\) The length of the pendulum is \(0.5~\text m\) and mass of the bob is \(1~\text{kg}\). The minimum value of \(\upsilon \) = __________ \(\text{m/s}\) so that the pendulum describes a circle.
(Assume the string to be inextensible and \(g=10\text{ m/s}^{2}\))

Q.

What is the mass formula in relation with force, energy, momentum?

Q.

A block of wood of mass M is suspended by means of a thread. A bullet of mass m is fired horizontally into the block with a velocity v. As a result of the impact, the bullet is embedded in the block. The block will rise to vertical height given by

1. $\frac{1}{2g}{\left(\frac{mv}{M+m}\right)}^2$

2. $\frac{1}{2g}{\left(\frac{mv}{M-m}\right)}^2$

3. $\frac{1}{2g}\frac{m{v}^2}{(M+m)}$

4. $\frac{1}{2g}\frac{m{v}^2}{(M-m)}$

Q. A bullet of mass $50\text{gm}$ is fired from a gun towards a ball of mass $450\text{gm}$


The bullet hits the ball with speed $200\text{m/s}$ in horizontal direction as shown in figure, and remains inside it. Find the magnitude of velocity of system of (ball+ bullet) after collision.

1. $50\text{m/s}$
2. $100\text{m/s}$
3. $20\text{m/s}$
4. $10\text{m/s}$

Q. Three particles of masses $1\text{Kg}$, $2\text{Kg}$ and $3\text{Kg}$ are situated at the corners of an equilateral triangle.
The speed of each particle is shown in the figure. Each particle maintains a direction towards the particle at the next corner symmetrically. The velocity of centre of mass of the system at this instant, if initially the system starts from rest, is:

1. $3{\text{ms}}^{-1}$
2. $5{\text{ms}}^{-1}$
3. $6{\text{ms}}^{-1}$
4. zero

Q. A block of wood of mass M is suspended by means of a thread. A bullet of mass m is fired horizontally into the block with a velocity v. As a result of the impact, the bullet is embedded in the block. The block will rise to vertical height given by

1. $\frac{1}{2g}{\left(\frac{mv}{M+m}\right)}^2$
2. $\frac{1}{2g}{\left(\frac{mv}{M-m}\right)}^2$
3. $\frac{1}{2g}\frac{m{v}^2}{M+m}$
4. $\frac{1}{2g}\frac{m{v}^2}{M-m}$

Q. A bag of mass $M$ hangs by a long thread and a bullet (mass $m$) comes horizontally with velocity $v$ and gets caught in the bag. Then for the combined system (bag + bullet) :

1. Momentum is $\frac{mMv}{(M+m)}$
2. KE is $\left(\frac{1}{2}\right)M{v}^2$
3. Momentum is $mv$
4. KE is $\frac{m^2{v}^2}{2(M+m)}$

Q.

A heavy ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at a speed of $60cm{s}^{-1}$on the string when the car is at rest and $62cm{s}^{-1}$ when the car accelerates on a horizontal road. Find the acceleration of the car. Take $g=10m{s}^{-2}$.

Q. A uniform rod of length $L$ lies on a smooth horizontal table. A particle moving on the table strikes the rod perpendicularly at an end and stops. Find the distance travelled by the centre of the rod by the time it turns through a right that of the particle, the collision is elastic

Q. A bullet of mass m is fired into a block of wood of mass M which hangs on the end of a pendulum and gets embedded into it. When the bullet strikes the wooden block, the pendulum starts swinging with maximum rise R. Then, the velocity of the bullet is given by.

1. $\frac{(M+m)gR}{m}$
2. $\frac{M+m}{m}\sqrt{2gR}$
3. $\frac{(M+m)\sqrt{\left(gR\right)}}{m}$
4. $\frac{M+m}{mgR}$

Q. A ball $B$ of mass $m$ is projected with some velocity from a block A of mass $2m$ kept on a smooth horizontal surface. The ball strikes the wall elastically and comes back to the block A. Find the distance of block A from the wall when ball reaches back to it. Velocity in $B$ is generated by a compressed spring fixed to block A. When the ball leaves spring, the distance of block from wall is $d$. (Neglect gravity)

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

Q. A ring of mass m and radius R has three particles attached to the ring as shown in the figure. The centre of the ring has a speed $v_0$. Find the kinetic energy of the system.(Slipping is absent).

Q. A bag (mass $M$) hangs by a long thread and a bullet (mass $m$) comes horizontally with velocity $v$ and gets caught in the bag, then for the combined ($bag+bullet$) system:

1. momentum is $\frac{mvM}{M+m}$
2. kinetic energy is $\frac{m{v}^2}{2}$
3. Mmomentum is $\frac{mv(M+m)}{M}$
4. Kinetic energy is $\frac{m^2{v}^2}{2(M+m)}$

Q.

A hollow sphere of mass $m$ = 1 kg and radius $R$ = 1 m rests on a smooth horizontal surface. A simple pendulum having string of length $R$ and bob of mass $m$ = 1 kg hangs from top most point of the sphere as shown in the figure. A bullet of mass $m$ = 1 kg and velocity $v$ = 2 m/s partially penetrates the left side of the sphere. The velocity of the sphere just after collision with bullet is:

1. 1 m/sec

2. 0.5 m/sec

3. 1.5 m/sec

4. 2 m/sec

Q.

A block of wood of mass M is suspended by means of a thread. A bullet of mass m is fired horizontally into the block with a velocity v. As a result of the impact, the bullet is embedded in the block. The block will rise to vertical height given by

1. $\frac{1}{2g}{\left(\frac{mv}{M+m}\right)}^2$

2. $\frac{1}{2g}{\left(\frac{mv}{M-m}\right)}^2$

3. $\frac{1}{2g}\frac{m{v}^2}{(M+m)}$

4. $\frac{1}{2g}\frac{m{v}^2}{(M-m)}$

Q. A block of wood of mass M is suspended by means of a thread. A bullet of mass m is fired horizontally into the block with a velocity v. As a result of the impact, the bullet is embedded in the block. The block will rise to vertical height given by

1. 
2. 
3. 
4. 

Q.

A hollow sphere of mass $m$ = 1 kg and radius $R$ = 1 m rests on a smooth horizontal surface. A simple pendulum having string of length $R$ and bob of mass $m$ = 1 kg hangs from top most point of the sphere as shown in the figure. A bullet of mass $m$ = 1 kg and velocity $v$ = 2 m/s partially penetrates the left side of the sphere. The velocity of the sphere just after collision with bullet is:

1. 1 m/s

2. 0.5 m/s

3. 1.5 m/s

4. 2 m/s

Q. A bullet of mass $m$ hits a target of mass $M$ hanging by a string and gets embedded in it. If the block rises to height $h$ as a result of this collision, the velocity of the bullet before collision is :

1. $v=\sqrt{2gh}$
2. $v=\sqrt{2gh}[1+\frac{m}{M}]$
3. $v=\sqrt{2gh}[1+\frac{M}{m}]$
4. $v=\sqrt{2gh}[1-\frac{m}{M}]$

Q. A ball of mass $m$ moving with velocity $v_0$ experiences a head-on elastic collision with one of the spheres of a stationary rigid dumbbell as shown in figure above. The mass of each sphere equals $\frac{m}{2}$, and the distance between them is $l$. Disregarding the size of the spheres, the proper angular momentum $\tilde{M}$ of the dumbbell after the collision, i.e. the angular momentum in the reference frame moving translationally and fixed to the dumbbell's center of inertia is given as $\tilde{M}=\frac{m{v}_{0}l}{x}$. Find $x$.

Q.

A hollow sphere of mass $m$ = 1 kg and radius $R$ = 1 m rests on a smooth horizontal surface. A simple pendulum having string of length $R$ and bob of mass $m$ = 1 kg hangs from top most point of the sphere as shown in the figure. A bullet of mass $m$ = 1 kg and velocity $v$ = 2 m/s partially penetrates the left side of the sphere. The velocity of the sphere just after collision with bullet is:

1. 1 m/s

2. 0.5 m/s

3. 1.5 m/s

4. 2 m/s

Q. A bag of mass $M$ hangs by a long thread and a bullet (mass $m$) comes horizontally with velocity $v$ and gets caught in the bag. Then for the combined system (bag + bullet) :

1. Momentum is $\frac{mMv}{(M+m)}$
2. KE is $\left(\frac{1}{2}\right)M{v}^2$
3. Momentum is $mv$
4. KE is $\frac{m^2{v}^2}{2(M+m)}$

Q. A smooth sphere of mass $M$ moving with velocity $u$ directly collides elastically with another sphere of mass $m$ at rest. After collision, their final velocities are $V$ and $v$ respectively. The value of $v$ is :

1. $\frac{2uM}{m}$
2. $\frac{2um}{M}$
3. $\frac{2u}{1+\frac{m}{M}}$
4. $\frac{2u}{1+\frac{M}{m}}$

Q. A block of mass $M=5\text{kg}$ is moving on a horizontal plane. An object of mass $m=1\text{kg}$ is dropped on to the block hitting it with a vertical velocity of $v_1=10\text{m/s}.$ The speed of the block at the same instant is $v_2=2\text{m/s}$ along the floor. The collision is momentary and the object sticks to the block upon collision. What will be the speed of the block just after the collision if the co-efficient of friction between the block and the horizontal plane is $\mathrm{0.4.}$

1. $1.4\text{m/s}$
2. $1.67\text{m/s}$
3. $1\text{m/s}$
4. $0.8\text{m/s}$

Q. A block of wood of mass M is suspended by means of a thread. A bullet of mass m is fired horizontally into the block with a velocity v. As a result of the impact, the bullet is embedded in the block. The block will rise to vertical height given by

1. $\frac{1}{2g}{\left(\frac{mv}{M+m}\right)}^2$
2. $\frac{1}{2g}{\left(\frac{mv}{M-m}\right)}^2$
3. $\frac{1}{2g}\frac{m{v}^2}{M+m}$
4. $\frac{1}{2g}\frac{m{v}^2}{M-m}$

Q. Assertion (A) : A body of "$m_1$" collides another body of mass "$m_2$" at rest elastically. The fraction of energy transferred to the second body is$\frac{m_1}{m_1+m_2}$
Reason (R) : In an "inelastic collision" only linear momentum is conserved

1. A is true but R is false
2. Both Assertion (A) and Reason (R) are correct but
   the reason does not give the correct explanation
3. Both Assertion (A) and Reason (R) are correct
   and R is the correct explanation
4. A is false but R is true

Q. A bullet of mass $50\text{gm}$ is fired from a gun towards a ball of mass $450\text{gm}$


The bullet hits the ball with speed $200\text{m/s}$ in horizontal direction as shown in figure, and remains inside it. Find the magnitude of velocity of system of (ball+ bullet) after collision.

1. $20\text{m/s}$
2. $10\text{m/s}$
3. $100\text{m/s}$
4. $50\text{m/s}$

Q. A block of mass $M=5\text{kg}$ is moving on a horizontal plane. An object of mass $m=1\text{kg}$ is dropped on to the block hitting it with a vertical velocity of $v_1=10\text{m/s}.$ The speed of the block at the same instant is $v_2=2\text{m/s}$ along the floor. The collision is momentary and the object sticks to the block upon collision. What will be the speed of the block just after the collision if the co-efficient of friction between the block and the horizontal plane is $\mathrm{0.4.}$

1. $1.4\text{m/s}$
2. $0.8\text{m/s}$
3. $1\text{m/s}$
4. $1.67\text{m/s}$

Q. A block of mass $M=5\text{kg}$ is moving on a horizontal plane. An object of mass $m=1\text{kg}$ is dropped on to the block hitting it with a vertical velocity of $v_1=10\text{m/s}.$ The speed of the block at the same instant is $v_2=2\text{m/s}$ along the floor. The collision is momentary and the object sticks to the block upon collision. What will be the speed of the block just after the collision if the co-efficient of friction between the block and the horizontal plane is $\mathrm{0.4.}$

1. $0.8\text{m/s}$
2. $1\text{m/s}$
3. $1.4\text{m/s}$
4. $1.67\text{m/s}$