Which of the following will have the greatest value of momentum amongst them?

An idle rock of mass

3 k g

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A body of mass

5 k g

moving with a speed of

1.5 m s^{- 1}

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15 k g

cycle moving with a speed of

0.8 m s^{- 1}

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600 g

ball moving with a speed of

18 m s^{- 1}

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Solution

The correct option is C $15 k g$ cycle moving with a speed of $0.8 m s^{- 1}$
Momentum is given by:
$p = m v$

Case I:
Mass of ball, $m_{b} = 600 g = 0.6 k g$
Velocity of ball, $v_{b} = 18 m s^{- 1}$
Momentum of ball, $p_{b} = 0.6 \times 18 = 10.8 k g m s^{- 1}$

Case II:
Mass of cycle, $m_{c} = 15 k g$
Velocity of cycle, $v_{c} = 0.8 m s^{- 1}$
Momentum of cycle, $p_{c} = 15 \times 0.8 = 12 k g m s^{- 1}$

Case III: As the velocity of rock is zero, its momentum will be zero.

Case IV:
Mass of the body = $5 k g$
Velocity of the body = $1.5 m s^{- 1}$
Momentum = $5 \times 1.5 = 7.5 k g m s^{- 1}$

Therefore out of the given cases, the cycle will have the greatest momentum.

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