A spring stores 5J of energy when stretched by 25 cm. It is kept vertical with the lower end fixed. A block fastened to its end is made to undergo small oscillations. If the block makes 5 oscillations each second what is the mass of the block?

Options

A. `m=0.16 kg`
B. `m=0.32 kg`
C. `k=160(N)/(m)`
D. `k=320(N)/(m)`

Answer

A, C

Explanation

Energy stored `=(1)/(2)kx^2=(1)/(2)kxx(0.25)^2=5J`
`k=160(N)/(m)`
period `T=2pisqrt((m)/(k))`
`T=(1)/(5)s`
`T^2=(4pi^2m)/(k)`
`(1)/(25)=(4pi^2m)/(160)`
`m=(4)/(25)kg` (As `pi^2=10`), hence `m=0.16kg`