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Question


PSolid sphere, QSolid cube,RSolid cone, SSolid cylinder

Assuming potential energy U at the ground level to be zero.
All objects are made of the same material.
UP=Potential energy of solid sphere
UQ=Potential energy of solid cube
UR=Potential energy of solid cone
US=Potential energy of solid cylinder
Identify the correct option(s).

A
US>UP
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B
UQ>US
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C
UP>UQ
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D
UP>US
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Solution

The correct option is B UQ>US
Since all are made of same material, density (ρ) is same for all. Potential energy of all bodies is given by,
U=MgYCM
where YCM= height of centre of mass

For sphere P :
MP=ρ×VP
MP=ρ×43π×(D2)3
YCM=D2
UP=ρ×43π×(D2)3×g×D2
UP=π12ρgD4

Similarly for cube Q:
MQ=ρ×VQ=ρ×D3
YCM=D2
UQ=ρ×D3×g×D2
UQ=12ρgD4

For cone R:
MR=ρ×13π×(D2)2×D
YCM=D4
UR=ρ×13π×(D2)2×D×g×D4
UR=π48ρgD4

For cylinder S:
MS=ρ×π×(D2)2×D
YCM=D2
US=ρ×π×(D2)2×D×g×D2
US=π8ρgD4

Comparing the potential energy of all bodies,
US>UP & UQ>US

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