A block of mass m is released on a smooth inclined plane of inclination 3 0 ∘ and mass M. Height of the block varies with time as h = 1.5 − 1.5 t 2 . ( h in metre & t = time in second). What is the ac

Question

A block of mass m is released on a smooth inclined plane of inclination 3 0 ∘ and mass M. Height of the block varies with time as h = 1.5 − 1.5 t 2 . ( h in metre & t = time in second). What is the acceleration of M ?

TestHub · Accepted Answer

Acceleration of block along incline (w.r.t. ground) $= \frac{mg s i n 3 0 ^{\circ}}{m} = g sin 3 0^{\circ} = 5 m s^{- 2}$

Vertical acceleration of block (w.r.t. ground) $= - \frac{d ^{2} h}{d t ^{2}} = 3 m s^{- 2}$

$5 = a cos 3 0^{\circ} + 3 cos 6 0^{\circ} \Rightarrow a = \frac{7}{3} m / s^{2}$

$tan 3 0^{\circ} = \frac{3}{a + a _{1}} \Rightarrow a + a_{1} = 33$

$a_{1} = 33 - \frac{7}{3} = \frac{2}{3} m / s^{2}$

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JEE Advanced (2028)