Question

The one end of rope is passing over a frictionless pulley is tied with a block of weight, W as shown in figure. The co-efficient of friction between the block and the horizontal plane is $\mu$. If the other end is allowed to pull without sliding the block, the maximum pull is permitted as

• A. $\frac{\mu Wsec\alpha }{(1+\mu tan\alpha )}$
• B. $\frac{\mu Wsec\alpha }{(1-\mu tan\alpha )}$
• C. $\frac{\mu Wcos\alpha }{(1+\mu tan\alpha )}$
• D. $\frac{\mu Wcos\alpha }{(1-\mu tan\alpha )}$

Answer 1

The correct option is A $\frac{\mu Wsec\alpha }{(1+\mu tan\alpha )}$



$\Sigma F_y=0\Rightarrow W=R+Tsin\alpha$ ....(i)

$\Sigma F_x=0\Rightarrow \mu R=Tcos\alpha$ ....(i)

From (i) and (ii)

$\therefore$ $T=\frac{\mu wsec\alpha }{(1+\mu Tan\alpha )}$