When a body slides down from rest along a smooth inclined plane making an angle of 30 ° with the horizontal, it takes time T . When the same body slides down from the rest along a rough inclined plane

Question

When a body slides down from rest along a smooth inclined plane making an angle of 30 ° with the horizontal, it takes time T . When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time α T , where α is a constant greater than 1 . The co-efficient of friction between the body and the rough plane is 1 x α 2 - 1 α 2 where x = _ _ _ _ _ _ _ _ _ _ .

TestHub · Accepted Answer

On smooth incline, a = g sin 30 ° by S = u t + 1 2 a t 2 S = 1 2 g 2 T 2 = g 4 T 2 . . . ( i ) On rough incline a = g sin 30 ° - μ g cos 30 ° by S = u t + 1 2 a t 2 S = 1 4 g ( 1 - 3 μ ) ( α T ) 2 . . . ( ii ) By ( i ) and ( ii ) 1 4 g T 2 = 1 4 g ( 1 - 3 μ ) α 2 T 2 ⇒ 1 - 3 μ = 1 α 2 ⇒ μ = α 2 - 1 α 2 1 3 ⇒ x = 3 . 00

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