First slide

making equation on system

Question

A block is released from rest from point A on a smooth track, whose cross section in vertical plane is quarter of a circle of radius ‘R’. The value of $θ$ for which the contact force between block and surface is equal to the weight of block is

Moderate

A

$\cos^{- 1} (\frac{2}{3})$
B

$\cos^{- 1} (\frac{1}{3})$
C

$\sin^{- 1} (\frac{2}{3})$
D

$\sin^{- 1} (\frac{1}{3})$

Solution

$\begin{array}{l} N - m g s i n θ = \frac{m v^{2}}{R} = \frac{m}{R} [2 g R \sin θ]; (V^{2} = 2 g h; h = r \sin θ) \\ \Rightarrow N = 3 m g \sin θ \\ \Rightarrow θ = \sin^{- 1} \frac{1}{3} i f N = m g \end{array}$

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