A cart of mass $M = 100 k g$ is at rest over a smooth horizontal surface. A boy of mass $m = 50 k g$ is standing over the cart. If he jumps from the cart with a horizontal velocity of $20 m s^{- 1}$ , the final velocity of the cart is :

10 m s^{- 1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

20 m s^{- 1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 10 m s^{- 1}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

- 20 m s^{- 1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $- 10 m s^{- 1}$
Given:
Mass of boy $(m_{1})$ = $50 k g$
Mass of cart $(m_{2})$ = $100 k g$
Initial velocity of boy $(u_{1})$ = $0 m s^{- 1}$
Initial velocity of cart $(u_{2})$ = $0 m s^{- 1}$
Final velocity of boy $(v_{1})$ = $20 m s^{- 1}$
Final velocity of cart $(v_{2})$ = $?$
According to the law of conservation of momentum,
Initial momentum of the system = Final momentum of the system
$\Rightarrow$ $m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}$
$\Rightarrow$ $0 + 0 = 50 \times 20 + 100 \times v_{2}$
$\Rightarrow$ $v_{2} = - 10 m s^{- 1}$

Negative sign indicates the velocity of cart is in opposite direction of the velocity of the boy.

Suggest Corrections

Similar questions

Q. A boy is running with a velocity of

2 m s^{- 1}

. He jumps over a stationary cart of

2 k g

while running. If the mass of the boy is of

20 k g

, find the velocity at which the cart moves after he jumps over the cart. (Neglect friction between the cart and ground)

Q. A boy is running with a velocity of

2 m s^{- 1}

. He jumps over a stationary cart of

2 k g

while running. If the mass of the boy is of

20 k g

, find the velocity at which the cart moves after he jumps over the cart. (Neglect friction between the cart and ground)

A boy of $50 k g$ mass is running with a velocity of $2 m s^{- 1}$ . He jumped into a stationary cart of $2 k g$ while running. Find the velocity of the cart after the boy jumped into it.

A boy of 50 kg is ruining with a velocity of 2m/s he jumps over a stationary of cart of 2kg while running find the velocity of cart after jumping of boy.

Q. A girl of mass

40 kg

jumps with horizontal velocity

5 m/s

onto a stationary cart of mass

3 kg

with frictionless wheels. Find her velocity as the cart starts moving.

Join BYJU'S Learning Program

A cart of mass M=100 kg is at rest over a smooth horizontal surface. A boy of mass m=50 kg is standing over the cart. If he jumps from the cart with a horizontal velocity of 20 ms−1, the final velocity of the cart is :

A cart of mass $M = 100 k g$ is at rest over a smooth horizontal surface. A boy of mass $m = 50 k g$ is standing over the cart. If he jumps from the cart with a horizontal velocity of $20 m s^{- 1}$ , the final velocity of the cart is :