Question

If a block moving up at $\theta ={30}^0$ with a velocity 5 m/s, stops after 0.5 sec, then $\mu$ is:

• A. 0.48
• B. 1.25
• C. 0.58
• D. none of the above

Answer 1

The correct option is C 0.58

The block experience a net retardation given by,

$a=-g(sin\theta +\mu cis\theta )$

The body starts with initial velocity.

$u=5m/s$ and initially comes to rest $(v=0)$

In time $t=0.5s$

using first law of kinematics,

$v=u+at$

$\Rightarrow 0=5-0.5g(sin\theta +ucos\theta )$

[Taking $g=10m/s^2$]

$\Rightarrow sin\theta +\mu cos\theta =1$

$\Rightarrow \mu =\frac{1-sin\theta }{cos\theta }=\frac{1}{\sqrt{3}}\simeq 0.58$