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  4. A wooden wedge of mass M and inclination angle α rests on a smooth floor. A block of mass m is kept on wedge. A force overset arrow P is applied on the wedge as shown in figure, such that a block remains stationary with respect to wedge. The magnitude of force overset arrow P is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-htyfs2xiyhvs.png />

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Q. A wooden wedge of mass $M$ and inclination angle $\alpha $ rests on a smooth floor. A block of mass $m$ is kept on wedge. A force $\overset{ \rightarrow }{P}$ is applied on the wedge as shown in figure, such that a block remains stationary with respect to wedge. The magnitude of force $\overset{ \rightarrow }{P}$ is

Question

NTA AbhyasNTA Abhyas 2020Laws of Motion

Solution:

Since, $P=\left(\right.M+m\left.\right)a$
Now as in free body diagram of block,
Solution
$macos \alpha = m g sin ⁡ \alpha \, $
$\therefore \, a=g\frac{sin \alpha }{cos ⁡ \alpha }=gtan ⁡ \alpha $ or $P=\left(M + m\right)gtan \alpha $