COM in Collision and Explosion

Q. An explosion breaks a rock into three parts. Two pieces go off at right angles to each other with 1.0 kg piece with a velocity of 12 m/s and other 2.0 kg piece with a velocity of 8 m/s. If the third piece flies off with a velocity of 40 m/s, compute the mass of the third piece.

1. 0.5 kg
2. 3 kg
3. 0.7 kg
4. 0.25kg

Q.

A ball of mass 50 g moving at a speed of 2.0 m/s strikes a plane surface at an angle of incidence ${45}^{\circ }$ . The ball is reflected by the plane at equal angle of reflection with the same speed. Calculate (a) the magnitude of the change in momentum of the ball (b) the change in the magnitude of the momentum of the ball.

1. zero, zero

2. 0 zero, 0.14 kg m/s

3. (a)0.14 kg m/s, 0.14 kg m/s

4. 0.14 kg m/s, zero

Q. A 30 kg projectile moving horizontally with a velocity ${\overrightarrow{v}}_0=\left(120m/s\right)\hat{i}$ explodes into two fragments A and B of masses 12 kg and 18 kg, respectively. Taking point of explosion as origin and knowing that 3 s later the position of fragment A is (300, 24, –48) m, determine the position of fragment B at the same instant.

1. (400, -91, 48)
2. (360, -91, 48)
3. (360, -45, 32)
4. (400, -91, 32)

Q.

Two balls with masses $m_1$ = 3 kg and $m_2$ = 5 kg have initial velocities $v_1$ = 5 m/s = $v_2$ in the directions as shown in figure. They collide at the origin. Find the velocity of the COM 3 seconds before collision?

1. -(12$\hat{i}-15\hat{j}$) m/s

2. (-12 $\hat{i}+15\hat{j}$) m/s

3. (-12 $\hat{i}+15\hat{j}$) m/s

4. (-15 $\hat{i}-12\hat{j}$) m/s

Q.

Light in certain cases may be considered as a stream of particles called "photons". Each photon has a linear momentum $\frac{h}{\lambda }$ where h is the Planck's constant and $\lambda$ is the wavelength of the light. A beam of light of wavelength $\lambda$ is incident on a plane mirror at an angle of incidence $\theta$. Calculate the change in the linear momentum of a photon as the beam is reflected by the mirror.

1. 

2. 

3. 

4. 

Q.

A man of mass 'M' having a bag of mass 'm' slips from the roof of a tall building of height 'H' and starts falling vertically (figure). When at a height 'h' from the ground, he notices that the ground below him is pretty hard, but there is a pond at a horizontal distance 'x' from the line of fall. In order to save himself he throws the bag horizontally (with respect to himself) in the direction opposite to the pond. Calculate the minimum horizontal velocity imparted to the bag so that the man lands in the water.

1. 

2. 

3. 

4. 

Q.

Figure shows a small block of mass 'm' which is started with a speed 'v' on the horizontal part of the bigger block of mass 'M' placed on a horizontal floor. The curved part of the surface shown is semicircular. All the surfaces are frictionless. Find the speed of the bigger block when the smaller block reaches the point A of the surface.

1. towards left

2. towards left

3. towards left

4. towards left

Q.

Two bodies A and B of mases m and 2m respectively are placed on a smooth floor. They 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 as shown in figure. At a certain instant of time $t_0$ after collision, it is found that the instantaneous velocities of A and B are the same. Further at this instant the compression of the spring is found to be $x_0$. Determine (a) the common velocity of A and B at time $t_0$ and (b) the spring constant.

1. $v=\frac{v_0}{3},k=\frac{2}{3}\frac{m{v}_0^2}{x_0^2}$

2. $v=\frac{v_0}{3},k=\frac{3}{4}\frac{m{v}_0^2}{x_0^2}$

3. $v=\frac{v_0}{2},k=\frac{2}{3}\frac{m{v}_0^2}{x_0^2}$

4. $v=\frac{v_0}{2},k=\frac{3}{4}\frac{m{v}_0^2}{x_0^2}$

Q.

A projectile is fired at a speed of 100 m/s at an angle of ${37}^{\circ }$ above the horizontal. At the highest point, the projectile breaks into two parts of mass in ratio 1 : 3, the smaller coming to rest. Find the distance from the launching point to the point where the heavier piece lands.

1. 1020 m

2. 920 m

3. 1220 m

4. 1120 m

Q.

A particle of mass m is projected from the ground with an initial speed $u_0$ at an angle $\alpha$ with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed $u_0$. The angle that the composite system makes with the horizontal immediately after the collision is ?

1. $\frac{\pi }{4}+\alpha$

2. $\frac{\pi }{4}$

3. $\frac{\pi }{4}-\alpha$

4. $\frac{\pi }{2}$