A body of mass 2kg moving with a speed of 4 m/s makes an elastic collision with another body at rest and continues to move in original direction but with one fourth of its initial speed. If the speed of centre of mass of the two bodies is $5^{x} \times 10^{- 1} m / s$ . Then the value of x is ____________.

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

answer is 2.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Conservation of linear momentum, $p_{i} = p_{f}$
$2 \times 4 = 2 \times 1 + m_{2} \times v_{2} m_{2} v_{2} = 6$
The coefficient of restitution, $e = \frac{v_{2} - v_{1}}{u_{1} - u_{2}}$
$1 = \frac{v_{2} - 1}{4} \Rightarrow v_{2} = 5 m / s$
By (i), $m_{2} \times 5 = 6 \Rightarrow m_{2} = 1.2 k g$

$v_{c m} = \frac{m_{1} v_{1} + m_{2} v_{2}}{m_{1} + m_{2}} = \frac{2 \times 1 + 1.2 \times 5}{2 + 1.2} = \frac{8}{3.2} = \frac{25}{10}$ $\Rightarrow x = 2$