Question

Two bodies $ A $ and $ B $ have masses $ 20\, kg $ and $ 5\, kg $ respectively. Each one is acted upon by a force of $ 4\, kg-wt $ . If they acquire the same kinetic energy in times $ {{t}_{A}} $ and $ {{t}_{B}}, $ then the ratio $ \frac{{{t}_{A}}}{{{t}_{B}}} $ is

• A. $ \frac{1}{2} $
• B. $ 2 $
• C. $ \frac{2}{5} $
• D. $ \frac{5}{6} $
• E. $ \frac{1}{5} $

Answer 1

Answer: (B)

Here, $m_{1}=20 kg , m_{2}=5 kg$, Force $=40 N$
$\therefore a_{1}=2 ms ^{-2}$ and $a_{2}=8 m s ^{-2}$
$\frac{1}{2} m_{1}\left(a_{1} t_{A}\right)^{2}=\frac{1}{2} m_{2}\left(a_{2} t_{B}\right)^{2}$
$\therefore 20 \times 4 \times t_{A}^{2}=5 \times 64 \times t_{B}^{2}$
$\therefore \frac{t_{A}^{2}}{t_{B}^{2}}=\frac{5 \times 64}{20 \times 4}=\frac{4}{1}$ or $\frac{t_{A}}{t_{B}}=2$