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Center of Mass question

2022 · 28 Jun · Shift 1 · Q65

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Center of Mass
2022 · 28 Jun · Shift 1 · Q65

Center of Mass question

2022 · 28 Jun · Shift 1 · Q65

JEE MainPhysicsCenter of MassNumerical+4 / −1

A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then, the trolly car starts moving with velocity 2 ms

-

1. The velocity of the running man was

\underline{\hspace{2cm}}

ms

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1, when he jumps into the car.

Numerical answer

View written solutionFree

Correct answer: 6

Identify the physical principle

When the man jumps into the stationary trolley and they move together afterward, this is a case of perfectly inelastic collision.

So, linear momentum is conserved.

Given data

Mass of man: $m_1 = 60\,\text{kg}$
Mass of trolley: $m_2 = 120\,\text{kg}$
Initial velocity of trolley: $u_2 = 0$
Final common velocity: $v = 2\,\text{m s}^{-1}$
Initial velocity of man: $u_1 = ?$

Apply conservation of momentum

Initial momentum = Final momentum

$m_1 u_1 + m_2 u_2 = (m_1 + m_2)v$

Substitute the values:

$60u_1 + 120(0) = (60+120)(2)$

$60u_1 = 180 \times 2$

$60u_1 = 360$

$u_1 = \frac{360}{60} = 6\,\text{m s}^{-1}$

Final answer

The velocity of the running man was

$\boxed{6}$

So the required integer answer is 6.

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