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40.A particle...

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40.A particle of mass m is kept on the top of a smooth sphere of radius R .it is given a sharp impulse which imparts it a horizontal speed V.what should be the minimum value of v for which the particle does not slip on the sphere?(with full reason)

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Q. A particle of mass

m

is kept on the top of a smooth sphere of radius

R

. It is given a sharp impulse which imparts it a horizontal speed

V

.
(a) Find the normal force between the sphere and the particle just after the impulse.

(b) What should be the minimum value of

V

for which the particle does not slip on the sphere?

(c)Assuming the velocity

v

to be half the minimum calculate in part,

(d) find the angle made by the radius.

Q. A particle of mass m is kept on the top of a smooth sphere of radius R. It is given a sharp impulse which imparts it a horizontal speed

ν

. (a) Find the normal force between the sphere and the particle just after the impulse. (b) What should be the minimum value of

v

for which the particle does not slip on the sphere? (c) Assuming the velocity

v

to be half the minimum calculated in part, (b) find the angle made by the radius through the particle with the vertical when it leaves the sphere.

Figure

Q. A solid sphere of mass m and radius R is placed on a plank of equal mass, which lies on a smooth horizontal surface. The sphere is given a sharp impulse in the horizontal direction so that it starts sliding with a speed of

v_{0}

. Find the time taken by the sphere to start pure rolling on the plank. The coefficient of friction between plank and sphere is

μ

.

Q. A particle is kept at rest at a distance

R

(earth's radius) above the earth's surface. The minimum speed with which it should be projected so that it does not return is

Q. A particle is kept at rest at a distance

R

(Earths radius) above the earths surface. The minimum speed with which it should be projected so that it does not return is

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