A point object of mass m is slipping down on a smooth hemispherical body of mass M and radius R. The point object is tied to a wall with an ideal string as shown. At a certain instant, speed of the hemisphere is v and its acceleration is a. Then speed vp and acceleration aP of a particle has value (Assume all the surfaces in contact are frictionless)

Foundation

Physics

Center of Mass

Constrained Relation

Constrained Motion

Question

A point object of mass m is slipping down on a smooth hemispherical body of mass M and radius R. The point object is tied to a wall with an ideal string as shown. At a certain instant, speed of the hemisphere is v and its acceleration is a. Then speed v_p and acceleration a_P of a particle has value (Assume all the surfaces in contact are frictionless)

a_P = a

$a_{P} = \sqrt{{[(\frac{v^{2}}{R}) + (a \frac{\sqrt{3}}{2})]}^{2} + {(\frac{a}{2})}^{2}}$

V_P = v sin 60°

V_P = v

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

x + Rθ = constant

$\frac{dx}{dt} + \frac{Rdθ}{dt} = 0$

$∴ ω = \frac{dθ}{dt} = \frac{v}{R}$

$α = \frac{dω}{dt} = \frac{a}{R}$

At θ = 60°,

$∴ V_{P} = {v and a}_{P} = \sqrt{{(\frac{a \sqrt{3}}{2} + \frac{v^{2}}{R})}^{2} + {(\frac{a}{2})}^{2}}$