Question

A 2 kg ball moving straight down strikes the floor at 8 m/s. It rebounds upwards at 6 m/s. the magnitude of change in momentum is
(A) 28 kg m/s
(B) 4 kg m/s
(C) 2 kg m/s
(D) 14 kg m/s​

Answer 1

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A 2 Kg ball is moving initially with a velocity 8 m/s strikes the floor rebounds upwards with a velocity 6 m/s. Find the change in momentum of the ball :

a) 28 Kg m/s

b) 4 Kg m/s

c) 2 Kg m/s

d) 14 Kg m/s

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From the Question,

• Mass of the ball (m) = 2 Kg

• Initial Velocity (u) = 8 m/s

• Final Velocity (v) = 6 m/s

To find

Change in momentum

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Let $\sf{P_{i}}$ and $\sf{P_{f}}$ be the initial and final momentums of the ball

$\large{\sf{P_{i}} = mu} \\ \\ \large{\hookrightarrow \ \sf{P_{i} = (2)(8)}} \\ \\ \huge{\hookrightarrow \ \boxed{\boxed{\sf{P_{i} = 16 \ Kg m{s}^{-1}}}}}$

$\large{\sf{P_{f}} = mv} \\ \\ \large{\hookrightarrow \ \sf{P_{f} = (2)(6)}} \\ \\ \huge{\hookrightarrow \ \boxed{\boxed{\sf{P_{f} = 12 \ Kg m{s}^{-1}}}}}$

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Change In Momentum

$\large{\sf{{P}_{f} - {P}_{i}}} \\ \\ \large{\longrightarrow 12 - 16 } \\ \\ \huge{\longrightarrow \ \tt{- 4 \ Kg.m{s}^{-1}}}$

Thus,the change in momentum of the ball is - 4 Kg m/s

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The negative sign indicates that the ball is moving in the direction of negative x - axis and emphasises the ball is losing velocity.

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Option (b) is correct

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Answer 2

Answer : 4 kg m/s

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Given :

• Mass of the ball = 2 kg
• Initial velocity ( u ) = 8 m/s
• Final velocity ( v ) = 6 m/s

To Find :

• The magnitude of change in momentum.

Formula used :

• $\sf\red{Change\:in\:momentum}= (mass\: \times initial\:velocity) - (mass\times final\:velocity)$

SolUtion :

First of all, put the given values in the formula.

We get,

$\sf ( 2\times 6) - (2\times 8)$

$\sf = 12 - 16$

$\sf = - 4\: kg\: m/s$

Here, ( - ) sign represents direction. We need only magnitude.

So,

The magnitude of change in momentum = 4 kg m/s.

Answer : Option B is correct.

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Do you know ?

• Nearly 74% of the atoms in the Milky Way galaxy are hydrogen atoms.
• Black holes are not black, they are dark .
• Gravity keeps Earth and the other planets in our solar system in orbit around the Sun.

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