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=|→g−→a
On applying ∑F=ma along vertical : Fb−T−mg=ma−−−−(1) ⇒ρwgeffV−T−mg=2×2 ⇒ρw×12×2ρs−T−2×10=4 ⎡⎢⎣geff=−10−2=−12 m/s2V=mρs;ρs→density of sphere⎤⎥⎦ ⇒T=10.5×12×2−20−4 [s=ρsρw=0.5] ⇒T=24 N
When thread snaps, Tension T acting on sphere is removed (T=0) ∴Fb−mg=ma
[From (1), a→ acceleration of sphere] ⇒ρwgeffV−mg=ma ⇒ρw×12×2ρs−2×10=2a ⇒12×20.5−20=2a ⇒a=14 m/s2
Therefore, option A and C are correct.