You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Instantaneous Velocity

A particle sl...

Question

A particle slides from the top of a smooth hemispherical surface of radius $R$ which is fixed on a horizontal surface. If it separates from the hemisphere at a height $h$ from the horizontal surface, then the speed of the particle is :

\sqrt{(2 g (R - h)}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\sqrt{(2 g (R + h))}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt{2 g R}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt{2 g h}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\sqrt{(2 g (R - h)}$
Energy conservation
$Δ P . E = Δ K . E$
$m g (R - h) = \frac{1}{2} m v^{2} - 0$
$v^{2} = 2 g (R - h)$
$v = \sqrt{2 g (R - h)}$

Suggest Corrections

Similar questions

A rocket is launched vertically from the surface of the earth of radius R with an initial speed v. If atmospheric resistance is neglected, the maximum height attained by the rocket is given by

Q. A small particle of mass

m

is projected horizontally from the top of a smooth and fixed hemisphere of radius

r

and speed

u

as shown in figure. For values of

u \geq u_{0} (u_{0} = \sqrt{g r})

the particle does not slide on the hemisphere (i.e; leaves the surface at the top itself). For

u = \frac{u_{0}}{3}

, the height from the ground at which the particle leaves the surface is

\frac{P r}{27}

. Then the value of P is .

Q. A particle starts sliding down from the top of the smooth convex hemisphere of radius

30

c m

, placed horizontally with convex side up. The vertical distance at which particle leaves the surface from it's highest point is:

Q. A particle is freely sliding down from the top of smooth convex hemisphere of radius

30 c m

. The particle leaves the surface at a vertical distance, from highest point, equal to:

Q. A particle slides down from the top outside smooth surface of a fixed sphere of radius a =

10

m. The initial horizontal velocity to be imparted to the particle 'at the top' is

5 K m / s

if it leaves the surface at a point whose vertical height above the center of sphere is

3 a / 4

. Find the value of K.

Join BYJU'S Learning Program

A particle slides from the top of a smooth hemispherical surface of radius R which is fixed on a horizontal surface. If it separates from the hemisphere at a height h from the horizontal surface, then the speed of the particle is :

The correct option is B √(2g(R−h)Energy conservationΔP.E=ΔK.Emg(R−h)=12mv2−0v2=2g(R−h)v=√2g(R−h)

A particle slides from the top of a smooth hemispherical surface of radius $R$ which is fixed on a horizontal surface. If it separates from the hemisphere at a height $h$ from the horizontal surface, then the speed of the particle is :

The correct option is B $\sqrt{(2 g (R - h)}$
Energy conservation
$Δ P . E = Δ K . E$
$m g (R - h) = \frac{1}{2} m v^{2} - 0$
$v^{2} = 2 g (R - h)$
$v = \sqrt{2 g (R - h)}$