Consider the system as shown in figure. The body of mass M = 3 kg leans against wall P placed at the bottom of an inclined plane of an angle α = 3 0 ∘ and a length s = 10 m . This body is connected by

Question

Consider the system as shown in figure. The body of mass $M = 3 kg$ leans against wall $P$ placed at the bottom of an inclined plane of an angle $α = 3 0^{\circ}$ and a length $s = 10 m$ . This body is connected by an inelastic string passed over an ideal pulley mounted at the top of the plane to another body of mass $m = 1 kg$ as shown. What should be horizontal velocity (in $m / sec$ ) of m so that the other the body (M) may detach from the wall, just after projection of m ?

(Take g = 10 m/s² )

TestHub · Accepted Answer

In order to assist the body of mass M to detach from the wall, the tension in the string must cancel the component of its weight along the incline.

$T_{limiting} = M.g. sin α$

At the moment when the body of mass $m$ is imparted a velocity $v$ (on the horizontal), a centrifugal force will act on it vertically downwards, because the body will perform a circular motion of radius. $h = s \cdot sin α . T = m \cdot g + F_{Cl}$ Where $F_{cl} = m \frac{V ^{2}}{s \cdot s i n α}$ , By making the calculations, we obtain

$v = s.g. sin α (\frac{M}{m} \cdot sin α - 1) = 10 \times 10 \times \frac{1}{2} [\frac{3}{1} \times \frac{1}{2} - 1] = 5 m / sec$

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JEE Advanced (2028)