Two blocks, one of mass A=1 kg and another B=2 kg are shown in figure. A force of 5 N is applied on A . Coefficient of friction between A and B is 0.2 and that between B and horizontal surface is zero. Find the time taken for the front face of A to coincide with that of B.

Question

Two blocks, one of mass A=1 kg and another B=2 kg are shown in figure. A force of 5 N is applied on A . Coefficient of friction between A and B is 0.2 and that between B and horizontal surface is zero. Find the time taken for the front face of A to coincide with that of B. (A)  2√2 s  (B)  √(8/3)s  (C)  √(3/8)s  (D)  2s

Tardigrade Admin · Accepted Answer

The free body diagram of two blocks is shown in figure

F - f = ma

o

F - μ N = ma

Or

5 - 0.2 \times 1 \times 10 = 1 \times a_{A}

Or

a_{A} = 3 m / s^{2}

This is the acceleration of

A

wrt

B

.
The time taken for the front surface of

A

to coincide with that of

B

is

s = u t + \frac{1}{2} a_{A} t^{2}

4 = 0 + \frac{1}{2} \times 3 \times t^{2}

Or

t^{2} = \frac{8}{3}

Or

t = \frac{8}{3} s

$22 s$

$\frac{8}{3} s$

$\frac{3}{8} s$

$2 s$

Q. Two blocks, one of mass A=1kg and another B=2kg are shown in figure. A force of 5N is applied on A. Coefficient of friction between A and B is 0.2 and that between B and horizontal surface is zero. Find the time taken for the front face of A to coincide with that of B.

22​s

38​​s

83​​s

2s

The free body diagram of two blocks is shown in figure F−f=ma o F−μN=ma Or 5−0.2×1×10=1×aA​ Or aA​=3m/s2 This is the acceleration of A wrt B. The time taken for the front surface of A to coincide with that of B is s=ut+21​aA​t2 4=0+21​×3×t2 Or t2=38​ Or t=38​​s

$22 s$

$\frac{8}{3} s$

$\frac{3}{8} s$

$2 s$