Same force acts on two bodies of different masses 3 kg and 5 kg initially at rest. The ratio of times required to acquire same final velocity is

Question

Same force acts on two bodies of different masses 3 kg and 5 kg initially at rest. The ratio of times required to acquire same final velocity is (A) 5: 3 (B) 25: 9 (C) 9: 25 (D) √3: √5

Tardigrade Admin · Accepted Answer

From Newton's second law F = (dp/dt) = (mv/t) ⇒ t = (mv/F) ⇒ (t1/t2) = (m1/m2) Given, m1 = 3 kg , m2 = 5 kg ∴ (t1/t2) = (3/5)

Q. Same force acts on two bodies of different masses 3 kg and 5 kg initially at rest. The ratio of times required to acquire same final velocity is

5 : 3

25 : 9

9: 25

$3 : 5$

3 : 5

From Newton's second law
$F = \frac{d p}{d t} = \frac{m v}{t} \Rightarrow t = \frac{m v}{F}$
$\Rightarrow \frac{t _{1}}{t _{2}} = \frac{m _{1}}{m _{2}}$
Given, $m_{1}$ = 3 kg , $m_{2}$ = 5 kg
$∴ \frac{t _{1}}{t _{2}} = \frac{3}{5}$