A block of mass m=0.1 kg is released from a height of 4 m on a curved smooth surface. On the horizontal surface, path AB is smooth and path BC is rough with a coefficient of friction μ =0.1 . If the impact of the block with the vertical wall at C is perfectly elastic, the total distance covered by the block on the horizontal surface before coming to rest will be (take g=10 m s- 2 )

Question

A block of mass m=0.1 kg is released from a height of 4 m on a curved smooth surface. On the horizontal surface, path AB is smooth and path BC is rough with a coefficient of friction μ =0.1 . If the impact of the block with the vertical wall at C is perfectly elastic, the total distance covered by the block on the horizontal surface before coming to rest will be (take g=10 m s- 2 ) <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-d6wvikycxnwo.png" /> (A) 29 m (B) 49 m (C) 59 m (D) 109 m

Tardigrade Admin · Accepted Answer

Total KE dissipated against friction =mgh=4J Work done against friction in one trip across BC=mgÎ¼× 2=0.2J ∴ Total number of trips across BC=(4/ text0.2)=20 ∴ Total distance =20× BC+19× AB=59m

$29 m$

$49 m$

$59 m$

$109 m$

Total $K E$ dissipated against friction $= m g h = 4 J$
Work done against friction in one trip across $BC = m gμ \times 2 = 0.2 J$
$∴$ Total number of trips across $BC = \frac{4}{0.2} = 20$
$∴$ Total distance $= 20 \times BC + 19 \times A B = 59 m$

29m

49m

59m

109m

Total KE dissipated against friction =mgh=4J Work done against friction in one trip across BC=mgμ×2=0.2J ∴ Total number of trips across BC=0.24​=20 ∴ Total distance =20×BC+19×AB=59m

$29 m$

$49 m$

$59 m$

$109 m$

Total $K E$ dissipated against friction $= m g h = 4 J$
Work done against friction in one trip across $BC = m gμ \times 2 = 0.2 J$
$∴$ Total number of trips across $BC = \frac{4}{0.2} = 20$
$∴$ Total distance $= 20 \times BC + 19 \times A B = 59 m$