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Question

A solid sphere of mass m=2 kg and specific gravity s=0.5 is held stationary relative to a tank filled with water. The tank is accelerating vertically upwards with 2 m/s2. Choose the correct option(s):


A
Tension is the thread is 24 N
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B
Tension in the thread is 28 N
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C
If the thread snaps, acceleration of the sphere is 14 m/s2
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D
If the thread snaps, acceleration of the sphere is 16 m/s2
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Solution

The correct option is C If the thread snaps, acceleration of the sphere is 14 m/s2
Let us suppose tension in the thread is T.
According to question,


We know for accelerated fluid in vertical direction,
Fb=ρwgeffV [For water]
Here, geff=|ga
On applying F=ma along vertical :
FbTmg=ma(1)
ρwgeffVTmg=2×2
ρw×12×2ρsT2×10=4
geff=102=12 m/s2V=mρs;ρsdensity of sphere
T=10.5×12×2204
[s=ρsρw=0.5]
T=24 N

When thread snaps, Tension T acting on sphere is removed (T=0)
Fbmg=ma
[From (1), a acceleration of sphere]
ρwgeffVmg=ma
ρw×12×2ρs2×10=2a
12×20.520=2a
a=14 m/s2
Therefore, option A and C are correct.

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