Question

In each of the three arrangements, the block of mass m₁ is being pulled left with constant velocity. All surfaces are smooth. The strings are light and inextensible and pulleys are massless. The ratio of the speed of the block of mass $m_2$ in the three cases respectively is:

• A. 2 : 1 : 4
• B. 2 : 4 : 1
• C. 4 : 2 : 1
• D. can not be calculated

Answer 1

The correct option is A

2 : 1 : 4

Let's assume that the velocity of $m_1$ towards left is 'v' in all cases.

Case I

Let the $m_1$ moves 'x' units leftwards then as string is inextensible, $m_2$ will also move x units upwards.

Velocity of $m_2$ in this case = v.

Cast II

In this case, by constraint relation, velocity of $m_2$ will be $\frac{v}{2}$

Case III

Again in this case if block $m_1$ moves left by x units then $m_2$ will move 2x upwards as string length is constant (constraint) therefore velocity of $m_2$ = 2v for this case

$\therefore$ $v_1$ : $v_2$ : $v_3$ = 1 : $\frac{1}{2}$ : 2 = 2 : 1 : 4