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Q.

If radius of earth is reduced to half without changing its mass, then match the following columns and markthe correct option from the codes given below.Column I (A) Angular velocity of earth(B) Time period of rotation of earth(C) Rotational kinetic energy of earthColumn II(p) will become two times(q) will become four times(r) will remain constant(s) None

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a

A  B  Cr s p

b

A  B  Cq   r  p

c

A  B  Cq   s   q

d

A  B  Cq  p  s

answer is C.

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Detailed Solution

L1=Iω=25MR2ωL2=25MR22ω'As,  L1=L2⇒ω'=4ω∴  2πT'=42πT⇒T=T4Further,  K=L22ISince, angular momentum is constant and I has become (1/4)th.Therefore, kinetic energy will become 4 times.Hence,  A→q,B→s,C→q
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If radius of earth is reduced to half without changing its mass, then match the following columns and markthe correct option from the codes given below.Column I (A) Angular velocity of earth(B) Time period of rotation of earth(C) Rotational kinetic energy of earthColumn II(p) will become two times(q) will become four times(r) will remain constant(s) None