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Questions  

A particle of mass m is attached at the end B of uniform rod of same mass m and length l. If the rod is whirled in vertical circle about end A, what is minimum speed of particle at end B, required to move it in vertical circle?

a
6gl
b
5gl
c
4gl
d
4.5gl

detailed solution

Correct option is D

For minimum speed supplied at bottom , at highest point  ω of rod should just become zero. Gain in PE = Loss in KEPE of Rod + PE of mass m=Rotational KE of rod+ KE of mass m⇒mg2l+mgl=12Iω2+12mu2​⇒mg2l+mgl=12ml23ul2+12mu2∵I=ml23⇒u=9gl2=4.5gl

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Similar Questions

The condition of equilibrium is satisfied when resultant of all forces acting on body vanishes and also no net torque acts on the body. However body can be different types of equilibrium as stable, unstable, neutral or may be having pure rotation when no resultant force acts on the body. Different conditions of equilibrium or rotational motion can be known by different types of energy it possesses. Column I mentions the state of body and column II mentions the type of energy it possesses. Match the correct options in two columns

COLUMN_I                                                             COLUMN_II

A)  Body in stable equilibrium                P) Rotational kinetic energy

 B)  Body in unstable equilibrium           Q) Minimum potential   

                                                                 energy

C)   Body in neutral equilibrium         R)Maximum potential energy

D) Body in pure rotational motion     S) Constant potential energy


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