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Question

Blocks of masses m, m,2m,4mand8m are arranged in a line on a frictionless floor. Another block of mass m, moving with speed v along the same line (see figure) collides with mass m in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass 8m starts moving the total energy loss is p% of the original energy. Value of ‘'p' is close to:


A

37

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B

77

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C

87

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D

94

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Solution

The correct option is D

94


Step 1: Given data

Masses of five blocks are m,m,2m,4m,8m

Step 2: Calculating final velocity

All the collisions are perfectly inelastic, so after the final collision, all blocks are moving together.

Let the final velocity will be v'.

Total mass after the collision=16m

From the conservation of momentum

Momentumbeforecollision=Momentumaftercollision

mv=16mv'

v'=v16

Step 3: Finding the value of p

Initial energy, Ei=12mv2

Final energy, Ef=12×16m×v162

Energyloss=Ei-Ef

=12mv2-12×16m×v162

=12mv21516

Percentageofenergyloss(p%)=EnergylossOriginalenergy×100

p%=12mv2151612mv2×100

p%=94%

Therefore, 94% of energy is lost by the time the last block of mass 8m starts moving.

Hence, the correct option is D.


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