Home › Maharashtra HSC Class 12 (Science) › physics › Rotational Dynamics › A solid sphere and a hollow sphere of equal mass…
A solid sphere and a hollow sphere of equal mass and radius roll without slipping with the same kinetic energy. The ratio of their linear speeds (solid : hollow) is
A1
B√(25/21)
C√(2/3)
D√(5/3)
Answer & Solution
Correct answer: B. √(25/21)
1. KE_roll = ½mv² + ½Iω² with ω = v/R. For solid sphere I = (2/5)mR² giving KE = (7/10)mv².
2. For hollow sphere I = (2/3)mR² giving KE = (5/6)mv².
3. Equating: (7/10)mv_s² = (5/6)mv_h². So v_s²/v_h² = (5/6)/(7/10) = 25/21.
4. Therefore v_s/v_h = √(25/21).
_Source: Maharashtra Balbharati Std XII Physics, Ch 1 "Rotational Dynamics" §1.8_
Related questions
A wheel of moment of inertia 2 kg·m² is accelerated from rest to 60 rad/s in 10 s. The torMoment of inertia of a thin uniform rod of mass M and length L about an axis through its cThe relation between linear velocity v, angular velocity ω and radius r in circular motionA car of mass 800 kg takes a turn of radius 40 m at 20 m/s on a level road. The minimum coCentrifugal force in a rotating frame is best described as aCentripetal force on a particle of mass m moving with speed v on a circle of radius r isA fan rotating at 90 rpm stops in 21 rotations under constant frictional torque. The time The direction of angular velocity vector of a rotating body is along the