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Question

A uniform disc of radius R is put over another uniform disc of radius 2R of same thickness and density. The peripheries of the two discs touch each other. The position of their center of mass is:

A
at R3 from the centre of the bigger disc towards the centre of the smaller disc
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B
at R5 from the centre of the bigger disc towards the centre of the smaller disc
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C
at 2R5 from the centre of the bigger disc towards the centre of the smaller disc
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D
at 2R5 from the centre of the smaller disc towards the centre of the smaller disc
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Solution

The correct option is B at R5 from the centre of the bigger disc towards the centre of the smaller disc

Given,

Smaller disc radius, =R

Larger disc radius, =2R

Density of disc =ρ

Thickness of disc=t

Mass of larger disc and smaller disc, mL & ms

Assume center of mass at distance x, from center of larger disc toward center of smaller disc.

From, formula of Center of Mass

ms×R+mL×0=(ms+mL)×x

x=ms×Rms+mL=ρ(πR2t)×Rρ(πR2t)+ρ[π(2R)2t]=R5

center of mass at distance R5, from center of larger disc toward center of smaller disc


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