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GATE 2016 ME (ME1) – Question 17

Engineering Mechanics · Impulse and momentum, energy formulations · 1 mark · Multiple choice

A point mass M is released from rest and slides down a spherical bowl (of radius R) from a height H as shown in the figure below. The surface of the bowl is smooth (no friction). The velocity of the mass at the bottom of the bowl is

Diagram for GATE 2016 ME (ME1) question 17
  1. $\sqrt{gH}$
  2. $\sqrt{2gR}$
  3. $\sqrt{2gH}$
  4. 0

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Show answer and explanation

Correct answer: (C) $\sqrt{2gH}$

Explanation

The normal reaction does no work and friction is absent. Conservation of mechanical energy gives MgH=(1/2)Mv². Cancelling mass yields **v=sqrt(2gH), C**. Bowl radius affects the path and normal reaction but not the speed for the stated vertical drop.