Question

When a block of mass $3kg$ is pushed by three persons from the left to the right, a constant acceleration of $0.2m{s}^{-2}$ is produced in the block. If five persons push the block in the same direction together, then the magnitude of the acceleration of the block will be: (Assume that each person applies equal force)

• A. $0.45m{s}^{-2}$
• B. $0.33m{s}^{-2}$
• C. $0.30m{s}^{-2}$
• D. $1m{s}^{-2}$

Answer 1

Answer: (B)

$0.33m{s}^{-2}$

Let each person applies a force of magnitude $F$ on the block from the left to the right.

$\underset{–}{\text{When three persons push the block:}}$

Total force on the block = $3F$

The acceleration of the block ($a_1$)=$0.2m/s^2$

The mass of the block is $m=3kg$

From Newton's second law of motion - $3F=m\times a_1=3\times 0.2=0.6N$

$\therefore F=\frac{0.6}{3}=0.2N$

$\underset{–}{\text{When five persons push the block:}}$

Total force on the block = $5F=5\times 0.2=1N$

The acceleration of the block is $a_2$

From Newton's second law of motion - $5F=m\times a_2=3\times a_2$

$\therefore a_2=\frac{5F}{3}=\frac{1}{3}=0.33N$