9th Class
Science
Force and laws of motion
Question Bank
Force and Laws of Motion
question_answer
In the arrangement shown in figure below, the ends P and Q of an stretchable string move downwards with uniform speed u. Pulleys A and B are fixed. Mass M moves upwards with a speed
A)\[2u\cos \theta \]
B)\[u\cos \theta \]
C)\[\frac{2u}{\cos \theta }\]
D)\[\frac{u}{\cos \theta }\]
Correct Answer:
D
Solution :
Referring figure, \[{{l}^{2}}={{b}^{2}}+{{y}^{2}}\] Differentiating with respect to time, we get \[2l\frac{dl}{dt}=2y\frac{dy}{dt}\] \[\Rightarrow \] \[\frac{dl}{dt}=\frac{ldy}{ydt}=\frac{1}{\cos \theta }\cdot \frac{dl}{dt}=\frac{u}{\cos \theta }\] (since as \[P\] and \[Q\] move down, the length\[l\]decreases at the rate of \[U\,\,m/s\])