A bullet of mass 1 kg fired with a speed 2 m s - 1 from x = 0 passes through a block of wood whose centre is kept at a distance of 10 m from the origin as shown in figure. The retarding force F r on the bullet within the wooden block is - 0 . 5 x . The minimum length of the block (upto one decimal digit) required to completely stop the bullet is (Assume e 4 = 55 )

Question

A bullet of mass 1 kg fired with a speed 2 m s - 1 from x = 0 passes through a block of wood whose centre is kept at a distance of 10 m from the origin as shown in figure. The retarding force F r on the bullet within the wooden block is - 0 . 5 x . The minimum length of the block (upto one decimal digit) required to completely stop the bullet is (Assume e 4 = 55 ), 10 . 1 m, 9 . 2 m, 9 . 7 m, 19 . 3 m

MARKS App · Accepted Answer

Given Mass of bullet m = 1 kg Velocity of bullet v = 2 m s - 1 The restoring force on the bullet within the block is F = - 0 . 5 x Applying work energy theorem, W = ∆ K E ⇒ ∫ F d x = - 1 2 m u 2 ⇒ ∫ x 1 x 2 F d x = ∫ x 1 x 2 - 0 . 5 x d x = - 1 2 × 1 × 2 2 ⇒ - 1 2 log e x 2 x 1 = - 2 ⇒ e 4 = x 2 x 1 = 10 - L / 2 10 + L / 2 = 55 ⇒ L = 19 . 3 m

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