Question

A particle of mass $0.01\text{kg}$ travels with a velocity given by $4\hat{i}+16\hat{k}{\text{ms}}^{-1}$. After sometime, its velocity becomes $8\hat{i}+20\hat{j}{\text{ms}}^{-1}$. The work done on particle during this interval of time is

• A. $0.32\text{J}$
• B. $6.9\text{J}$
• C. $9.6\text{J}$
• D. $0.96\text{J}$

Answer 1

The correct option is D $0.96\text{J}$

Magnitude of initial velocity of particle is,
$v_i=\sqrt{4^2+{16}^2}=\sqrt{272}\text{m/s}$
Magnitude of final velocity of particle is,
$v_f=\sqrt{8^2+{20}^2}=\sqrt{464}\text{m/s}$
From work energy theorem,
$W_{\text{ext}}=\Delta KE$
$W_{\text{ext}}=\frac{1}{2}m(v_f^2-v_i^2)$
$W_{\text{ext}}=\frac{1}{2}\times 0.01\times (464-272)$
$\therefore W_{\text{ext}}=0.96\text{J}$