Question

A small particle of mass m starts sliding down form rest along the smooth surface
of a fixed hollow hemisphere of mass M (4m). the distance of center of mass of
(particle + hemisphere) from center o of hemisphere, when the particle separates
from the surface of hemisphere is R. Find the value of 'a'
V60
Fixed​

Answer 1

Concept introduction:

Explanation:

Final answer:

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Answer 2

Concept:

The entire mechanical energy of a system is conserved, meaning it cannot be generated or destroyed and can only change internally from one form to another when conservative forces are acting on the system.

Given:

Mass = m

Hemisphere mass = 4m

Radius of hemisphere = R

Find:

Height from which the block will leave hemisphere.

Solution:

mgcosθ - N = mV² / R

if Body is detached then N = 0

mgcosθ = mv²/R

cosθ = v²/Rg ---1

Applying conservation of mechanical energy

KEi + PEi = KEf + Uf

0 + mgR(1 - cosθ) = (1/2)mv² + 0

2(1 - cosθ) = v²/Rg ---2

From 1 and 2

2 - 2 cosθ = cosθ

Cosθ = 2/3

So height h = Rcosθ

h = R×(2/3)

h = 2R/3

Hence, the Height from which the block will leave hemisphere will be 2R/3.

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