A hemispherical bowl of radius r = 0.1m is rotating about its axis (which is vertical) with an angular velocity 
. A particle of mass 10 -2 kg on the frictionless inner surface of the bowl is also rotating with the same 
. the particle is at a height h from the bottom of the bowl.
A
Obtain the relation between h and 
. What is the minimum value of 
needed in order to have a nonzero value of h.
. What is the minimum value of needed in order to have a nonzero value of h.
B
It is desired to measure ‘ g ’ using this setup by measuring h accurately. Assuming that r and 
are known precisely and that the least count in the measurement of h is 10 -4 m. What is minimum error g in the measured value of g. [g = 9.8m/s 2 ]
are known precisely and that the least count in the measurement of h is 10 -4 m. What is minimum error g in the measured value of g. [g = 9.8m/s 2 ]
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
-9.8 x 10 -3 m/s 2
Sol.
∴ tan θ = 
⇒ 
= 
⇒ ω 2 = g/ (r – h) ......(1)
h > 0 ⇒ r – 
> 0
⇒ ω > 
= 
= 
= 
rad/second Ans.
g = ω 2 (r – h)
= – 
maximum value of h is 0.1 so that Δ g = – 
= – 9.8 × 10 – 3 m/s 2
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