NEET 2010 Physics - Class 11 AIPMT-2010-Ph-2040 Solution: A gramophone record is revolving with an angular velocity \(…

QAIPMT-2010-Ph-2040: NEET 2010 Physics - Class 11 AIPMT-2010-Ph-2040 Solution: A gramophone record is revolving with an angular velocity \(…

A gramophone record is revolving with an angular velocity

\omega

. A coin is placed at a distance r from the centre of the record. The static coefficient of friction is

\mu

. The coin will revolve with the record if

r = \mu g\omega^2

r < \frac{\mu g}{\omega^2}

r \le \frac{\omega^2}{\mu g}

r \ge \frac{\mu g}{\omega^2}

Multiple Choice Options

A ${1 \over 2}{{I_b^2} \over {\left( {{I_t} + {I_b}} \right)}}\omega _i^2$ 2 1 _ ( I t _ + I b _ ) I b 2 _ _ _ i 2 _
B ${1 \over 2}{{I_t^2} \over {\left( {{I_t} + {I_b}} \right)}}\omega _i^2$ 2 1 _ ( I t _ + I b _ ) I t 2 _ _ _ i 2 _
C ${{{I_b} - {I_t}} \over {\left( {{I_t} + {I_b}} \right)}}\omega _i^2$ ( I t _ + I b _ ) I b _ _ I t _ _ _ i 2 _
D ${1 \over 2}{{{I_b}{I_t}} \over {\left( {{I_t} + {I_b}} \right)}}\omega _i^2$ 2 1 _ ( I t _ + I b _ ) I b _ I t _ _ _ i 2 _

Step-by-Step Verified Solution

As no external torque is applied to the system, the angular momentum of the system remains conserved. _ L i = L f According to given problem, I t _ i = ( I t + I b ) _ f _ _ f = I t _ i ( I t + I b ) ...(i) Initial energy, E i = 1 2 I t _ i 2 ...(ii) Final energy, E f = 1 2 ( I t + I b ) _ f 2 ...(iii) Substituting the value of _ f from equation (i) in equation (iii), we get Final energy, E f = 1 2 ( I t + I b ) ( I t _ i ( I t + I b ) ) 2 = 1 2 I t 2 _ i 2 I t + I b ...(iv) Loss of energy, _ E = E i � E f = 1 2 I t _ i 2 _ 1 2 I t 2 _ i 2 ( I t + I b ) (Using (ii) and (iv)) = _ i 2 2 ( I t _ I t 2 ( I t + I b ) ) = _ i 2 2 ( I t 2 _ I b I t _ I t 2 ( I t + I b ) ) = 1 2 I b I t ( I t + I b ) _ i 2

QAIPMT-2010-Ph-2040: NEET 2010 Physics - Class 11 AIPMT-2010-Ph-2040 Solution: A gramophone record is revolving with an angular velocity \(…

Multiple Choice Options

Step-by-Step Verified Solution

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