Worksheets on Acceleraion due to gravity (class 11)

WORKSHEET NO:1

Acceleration due to Gravity

Consider a body of mass m, placed on the surface of earth of mass M and radius R.

v What is the force of gravity acting on the body,

·        According to Newton’s  second laaw of motion?

·        According to Newton’s universal law of gravitation?

v From the two equations can you formulate the equation for acceleration due to gravity ,g ?

v Is the value of ‘g’ depends the mass of the body ?

v Is it a vector quantity or a scalar quantity ?

v Can you find out the value of ‘g’ ?

WORKSHEET NO:2

Variation of ‘g’ with altitude(h)

Consider a body of mass m lying on the surface of earth of mass M and radius R. Let ’g’ be the acceleration due to gravity on the surface of earth.

Let the body be taken to a height ‘h’ above the surface of earthh where the value of acceleration due to gravity is g_h.

Ø How do you calculate ‘g’?

Ø What about ‘g_h’ ?

[Hint: replace ‘R’ with (R+h) in the equation for ‘g’ ]

Ø How the acceleration due to gravity varies with hight ?

[ Hint: divide g_h by g ]

Ø If h<<< R , how the value of g varies ?

WORKSHEET No : 3

Variation of ‘g’ with Depth (d)

Assume the earth to be homogeneous (having uniform density) of radius R and mass M. Let ‘ƿ’ be the mean density of earth. Consider a body of mass ‘m’ lying on the surface of earth at a place where g is the acceleration due to gravity.

·        What is the mass of earth ?

[Hint : earth is assumed to be a homogeneous sphere]

·        How do you calculate the value of g at the surface of earth ?

Now let the body be taken to a depth ‘d’ below the surface of earth where the value of acceleration due to gravity is ‘g_d’.

·        Can you find out the radius of inner sphere?

·        From the figure, can you say which sphere contribute acceleration to the object ‘M’?

·        Calculate the equation for ‘g_d’.

·        From the equations, can you find out how g varies with the depth (d)?