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Question

In spring-block system match the following columns.

Column IColumn II(A) If k (the spring constant) is made 4 times(p) Angular speed will become 16 times(B) If m (the mass of block) is made 4 times(q) Potential energy will become 4 times(C) If k and m both are made 4-times(r) Kinetic energy will remain unchanged(s) None

A
As,Bq,Cq
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B
Aq,Br,Cq
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C
Aq,Bs,Cr
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D
Ar,Bp,Cs
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Solution

The correct option is C Aq,Bs,Cr
a) We know that, ω=Km
If K is made 4 times, then ω=4Km
ω=2Km ...(1)
Potential energy (U)=12mω2x2=12Kx2 ...(2)
Using (1),
U=12mω2x2
=12m(4×Km)x2
=4(12Kx2)
=4U
If K is made 4 times, then potential energy will become 4 times.

b) If m is made 4 times. then ω=K4m
ω=12Km
potential energy u=14(12mω2x2)=U4

c)If K and m both are made 4 times then ω remains same Kinetic energy will remain unchanged.

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