Question

In the arrangement shown in figure (3-Q3), the ends P and Q of an inextensible string move downwards with uniform speed u. Pulleys A and B are fixed. The mass M moves upwards with a speed.

(a) 2u cosθ

(b) u/cosθ

(c) 2u/cosθ

(d) ucosθ .

Answer 1

(b) u/cosθ.

Explanation :

Speed of Q is u downwards so in unit time it goes distance u downwards. Since the strings are in-extensible the other end of the string near mass M will shorten by a length of u. Consider the portion of above figure as shown below.

When Q moves to Q', X should move to X' so that QQ'=XX'=u. But the mass moves upwards, so X will actually move upwards to Y so as BX'=BY. For the small angle X'BY the line X'Y 丄 XX'. So ΔXX'Y is a right angled triangle. (XX'/XY)=Cosθ XY=(XX'/Cosθ) = u/Cosθ It is the distance traveled by mass M in unit time ie, speed of M. Hence the answer.