Two blocks identical in shape and size but made of different materials are acted upon equal forces which cause them to slide on a horizontal surface. The acceleration of the second block is found to be 3 times that of the first. What is the ratio of the mass of the second to the first?

m₂/m₁ =5/1

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m₂/m₁ = 1/3

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m₂/m₁= 3/1

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m₁/ m₂ = 2/1

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Solution

The correct option is B
m₂/m₁ = 1/3

Step 1: Calculate the ratio of acceleration of both the blocks

Let, mass of the first block = $m_{1}$

Acceleration of the first block = $a_{1}$

Mass of the second block = $m_{2}$

Acceleration of the second block = $a_{2}$

Also, $a_{2}$ = 5 $a_{1}$

Step 2: Calculate the mass ratio for the blocks

If the force acting on each block is F, then

F = $m_{1}$ $a_{1}$ and F = $m_{2}$ $a_{2}$ = $m_{2}$ $\times$ 3 $a_{1}$

or $m_{1}$ $a_{1}$ = $m_{2}$ $a_{2}$ = $m_{2}$ $\times$ 3 $a_{1}$

or $m_{1}$ = 3 $m_{2}$

Thus, the mass of the second block is one-third that of the first block.

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