Question

A cart is being pulled up the incline, using a motor $M$ and an ideal pulley and ideal rope arrangement as shown in figure. Then the speed of point ${}^{\prime }{P}^{\prime }$ of the string with which it moves so that the car moves up the inclined plane with a constant speed of $V_{cart}=$2 m/s is (Incline is at rest):

• A. $12m{s}^{-1}$
• B. $3m{s}^{-1}$
• C. $5m{s}^{-1}$
• D. $6m{s}^{-1}$

Answer 1

The correct option is D $6m{s}^{-1}$

We can see that three segments of the string which is supporting the cart is balanced by a single segment of string from motor M. So from pulley constraint relation, for a small displacement, $x$ of string towards motor would produce $x^{\prime }=3x$ displacement of cart.

Therefore $x^{\prime }=3x$

Differentiating, $v^{\prime }=3v$
Therefore, velocity of point P$=3\times 2=6$ m/s