Question

A block is kept on a frictionless inclined surface with angle of inclination $\alpha$. The incline is given an acceleration ${}^{\prime }{a}^{\prime }$ to keep the block stationary. Then ${}^{\prime }{a}^{\prime }$ is equal to:-

• A. $\frac{g}{\tan \alpha }$
• B. $g\cos ec\alpha$
• C. $g$
• D. $g\tan \alpha$

Answer 1

The correct option is D $g\tan \alpha$

$\begin{array}{c}\text{Correct option is}\left(D\right)\\ \text{Applying pseudo force;}\\ \begin{array}{c}P=m_B{a}_W\\ m_B\Rightarrow \text{mass of block}\\ a_{\omega }\Rightarrow \text{acceleration of wedge}\\ \text{Balancing forces on block along wedge:}\\ \text{ma}\cos \alpha =\mathrm{mg}\sin \alpha \\ a=g\tan \alpha \end{array}\end{array}$