A small cubical block of mass 1 kg is placed inside a rough rectangular groove made in a circular rough table as shown in the figure. Coefficient of friction for all the rough surfaces is μ = 0.5 . Th

Question

A small cubical block of mass 1 kg is placed inside a rough rectangular groove made in a circular rough table as shown in the figure. Coefficient of friction for all the rough surfaces is $μ = 0.5$ . The table starts rotating clockwise with angular acceleration $1 rad / sec^{2}$ in a horizontal plane about its axis. Find the time (in sec) after which the block will start motion with respect to table. Assume the size of block slightly smaller then the width of groove.

TestHub · Accepted Answer

t , ω = ω 0 ​ + a t = t The block starts to slide if the resultant of − ( m a c ​ + m a T ​ ) + N 2 ​ becomes greater than the maximum total friction. ⇒ m ω 2 r cos 3 7 ∘ − m α r cos 5 3 ∘ > μ ( m ω 2 r sin 3 7 ∘ + m α r sin 5 3 ∘ ) + μ m g ⇒ 5 4 t 2 ​ − 5 3 ​ > 2 1 ​ [ 5 3 ​ t 2 + 5 4 ​ + r g ​ ] ⇒ t 2 > 4 ⇒ t > 2 sec .

Physics - Circular Motion Question with Solution | TestHub

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JEE Advanced 2028 (Class 11)