A particle is given a certain velocity v at point P as shown on a hemispherical smooth surface. What is the value of v (in m / s ) such that when the particle reaches point Q, the normal reaction of the surface becomes equal to the weight of the particle? (Radius of hemisphere, R=1.6 m, g=10 m / s 2 )

Question

A particle is given a certain velocity v at point P as shown on a hemispherical smooth surface. What is the value of v (in m / s ) such that when the particle reaches point Q, the normal reaction of the surface becomes equal to the weight of the particle? (Radius of hemisphere, R=1.6 m, g=10 m / s 2 ) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

N=m g ⇒ vf=0 m g (R/2)=(1/2) m vi2 ⇒ v=√g R=4 m / s

Q. A particle is given a certain velocity v at point P as shown on a hemispherical smooth surface. What is the value of v (in m/s ) such that when the particle reaches point Q, the normal reaction of the surface becomes equal to the weight of the particle? (Radius of hemisphere, R=1.6m,g=10m/s2 )

N=mg ⇒vf​=0 mg2R​=21​mvi2​ ⇒v=gR​=4m/s

$N = m g$
$\Rightarrow v_{f} = 0$
$m g \frac{R}{2} = \frac{1}{2} m v_{i}^{2}$
$\Rightarrow v = g R = 4 m / s$