Figure shows two blocks A and B having mass 2 kg and 4 kg moving with a speed 4 m/sec and 2 m/sec respectively. The maximum compression in the spring and final velocity of 2kg block are respectively.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$\sqrt{\frac{24}{45}} m, 3 m / s$

$\sqrt{\frac{24}{25}} m, 3 m / s$

$\sqrt{\frac{24}{45}} m, 4 / 3 m / s$

$\sqrt{\frac{24}{25}} m, 8 / 3 m / s$

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\frac{1}{2} μ v_{r}^{2} = \frac{1}{2} k x^{2}$
$\begin{array}{l} x = V_{r e r}^{2} \sqrt{\frac{μ}{k}} \\ = 2 \times \sqrt{\frac{8 / 6}{10}} = \sqrt{\frac{8}{15}} \end{array}$
From conservation of momentum
$\begin{array}{l} 2 \times 4 + 4 \times 2 = 2 v_{1} + 4 v_{2} \\ 8 = v_{1} + 2 v_{2} \end{array}$
From conservation of energy
$\frac{1}{2} \times 2 \times 4^{2} + \frac{1}{2} \times 4 \times 2^{2} = \frac{1}{2} \times 2 \times v_{1}^{2} + \frac{1}{2} \times 4 \times v_{2}^{2}$ …… (ii)
On solving $v_{1} = \frac{4}{3} m / s, v_{2} = \frac{10}{3} m / s$