Question

A block of mass m is released from the top of a rough inclined plane as shown in the figure. Coefficient of friction between the block and the plane is $\mu$. Speed of the block at the bottom of the plane is v.

• A. Block will reach bottom if $l\ge \mu d$
• B. Work done by friction is independent of l
• C. Work done by friction is independent of d
• D.
  $v=\sqrt{2g(l-\mu d)}$

Answer 1

Answer: (A), (B), (D)

$v=\sqrt{2g(l-\mu d)}$



$f_l=\mu N=\mu mgcos\theta$
$w_f=\int fdl=\int umgcos\theta dl$
$w_f=\int umgdx=\mu mgd$
By work energy theorem, $\Rightarrow mgl-\mu mgd=\frac{1}{2}m{v}^2$
$\Rightarrow v=\sqrt{2g(l-\mu d)}$