r is the radius of the earth and omega is its angular

$$R$$ is the radius of the earth and $$\omega $$ is its angular velocity and $${g_p}$$ is the value of $$g$$ at the poles. The effective value of $$g$$ at the latitude $$\lambda = {60^ \circ }$$ will be equal to

A. $${g_p} - \frac{1}{4}R{\omega ^2}$$

B. $${g_p} - \frac{3}{4}R{\omega ^2}$$

C. $${g_p} - R{\omega ^2}$$

D. $${g_p} + \frac{1}{4}R{\omega ^2}$$

Answer : $${g_p} - \frac{1}{4}R{\omega ^2}$$

Solution :
$$\eqalign{ & g = {g_p} - R{\omega ^2}{\cos ^2}\lambda \cr & = {g_p} - {\omega ^2}R{\cos ^2}{60^ \circ } = {g_p} - \frac{1}{4}R{\omega ^2} \cr} $$

Releted MCQ Question on
Basic Physics >> Gravitation

Releted Question 1

If the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would-

A. Decrease

B. Remain unchanged

C. Increase

D. Be zero

View Answer

Releted Question 2

If $$g$$ is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass $$m$$ raised from the surface of the earth to a height equal to the radius $$R$$ of the earth, is-

A. $$\frac{1}{2}\,mgR$$

B. $$2\,mgR$$

C. $$mgR$$

D. $$\frac{1}{4}mgR$$

View Answer

Releted Question 3

If the distance between the earth and the sun were half its present value, the number of days in a year would have been-

A. $$64.5$$

B. $$129$$

C. $$182.5$$

D. $$730$$

View Answer

Releted Question 4

A geo-stationary satellite orbits around the earth in a circular orbit of radius $$36,000 \,km.$$ Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface $$\left( {{R_{earth}} = 6400\,km} \right)$$ will approximately be-

A. $$\frac{1}{2}\,hr$$

B. $$1 \,hr$$

C. $$2 \,hr$$

D. $$4 \,hr$$

View Answer

$$R$$ is the radius of the earth and $$\omega $$ is its angular velocity and $${g_p}$$ is the value of $$g$$ at the poles. The effective value of $$g$$ at the latitude $$\lambda = {60^ \circ }$$ will be equal to

Releted MCQ Question on
Basic Physics >> Gravitation

If the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would-

If $$g$$ is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass $$m$$ raised from the surface of the earth to a height equal to the radius $$R$$ of the earth, is-

If the distance between the earth and the sun were half its present value, the number of days in a year would have been-

A geo-stationary satellite orbits around the earth in a circular orbit of radius $$36,000 \,km.$$ Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface $$\left( {{R_{earth}} = 6400\,km} \right)$$ will approximately be-

Practice More Releted MCQ Question on
Gravitation

Practice More MCQ Question on Physics Section

$$R$$ is the radius of the earth and $$\omega $$ is its angular velocity and $${g_p}$$ is the value of $$g$$ at the poles. The effective value of $$g$$ at the latitude $$\lambda = {60^ \circ }$$ will be equal to

Releted MCQ Question on Basic Physics >> Gravitation

If the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would-

If $$g$$ is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass $$m$$ raised from the surface of the earth to a height equal to the radius $$R$$ of the earth, is-

If the distance between the earth and the sun were half its present value, the number of days in a year would have been-

A geo-stationary satellite orbits around the earth in a circular orbit of radius $$36,000 \,km.$$ Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface $$\left( {{R_{earth}} = 6400\,km} \right)$$ will approximately be-

Practice More Releted MCQ Question on Gravitation

Practice More MCQ Question on Physics Section

Releted MCQ Question on
Basic Physics >> Gravitation

Practice More Releted MCQ Question on
Gravitation