Question

In the arrangement shown in the figure, the ends P and Q of
an unstretchable string move downwards with uniform
speed U. Pulleys A and B are fixed. Mass M moves
upwards with a speed

• A. $2Ucos\theta$
• B. $\frac{U}{cos\theta }$
• C. $\frac{2U}{cos\theta }$
• D. Ucos$\theta$

Answer 1

Answer: (B)

In the right angle $\Delta$PQR
$t^2=c^2+y^2$
Differentiating this
equation with respect to
time, we ge
$2t\frac{dl}{dt}=0+2y\frac{dy}{dt}$
or $(-\frac{dy}{dt})=\frac{l}{y}(-\frac{dl}{dt})$
$Here,-\frac{dy}{dt}=v_M\Rightarrow \frac{1}{y}=\frac{1}{cos\theta }$
and -dl / dt =U
Hence,$v_M=\frac{U}{cos\theta }$
$\therefore$ Correct option is (b).
Hence ,$v_M=\frac{U}{cos\theta }$ $\therefore$ Correct option is (b).