Write true or false for the following statements:Acceleration due to g

1.	Write true or false for the following statements:Acceleration due to gravity is expressed asg =G\(\frac{M}{R^2}\)Where, symbols have their usual meanings.
Answer» True Explanation: The acceleration produced in a freely falling body by the gravitational pull of the earth is called the acceleration due to gravitation. We know that, Force = Mass × Acceleration F = m × a a = \(\frac{F}{m}\)............1 Where, F is the force on the object of mass m dropped from a distance r from the centre of earth of mass M. So, force exerted by the earth on the object is F = G\(\frac{M\times m}{r^2}\).............2 M = Mass of Earth m = mass of object r = distance of object from centre of earth Now, from equation 1 and 2, a =G\(\frac{M\times m}{r^2\times m}\) a =G\(\frac{M}{r^2}\) Now, from above, a = g = Acceleration due to gravity Hence, g = G\(\frac{M}{r^2}\)

Write true or false for the following statements:Acceleration due to gravity is expressed asg =G\(\frac{M}{R^2}\)Where, symbols have their usual meanings.

Answer»

True

Explanation: The acceleration produced in a freely falling body by the gravitational pull of the earth is called the acceleration due to gravitation.

We know that,

Force = Mass × Acceleration

F = m × a

a = \(\frac{F}{m}\)............1

Where, F is the force on the object of mass m dropped from a distance r from the centre of earth of mass M.

So, force exerted by the earth on the object is

F = G\(\frac{M\times m}{r^2}\).............2

M = Mass of Earth

m = mass of object

r = distance of object from centre of earth

Now, from equation 1 and 2,

a =G\(\frac{M\times m}{r^2\times m}\)

a =G\(\frac{M}{r^2}\)

Now, from above,

a = g = Acceleration due to gravity

Hence,

g = G\(\frac{M}{r^2}\)

Discussion

No Comment Found

Related InterviewSolutions

Explain why a long pole is more beneficial to the tight rope walker if the pole has slight bending.
Assertion : Even when orbit of a satellite is elliptical, its plane of rotation passes through the centre of earth. Reason: According to law of conservation of angular momentum plane of rotation of satellite always remin same.A. If both the assertion and reason are true and reason is a true explantion of the assertion.B. If both the assertion and reason are true but the reason is not true the correct explantion of the assertion.C. If the assertion is true but reason falseD. If both the assertion and reason are false.
Assertion : Even when orbit of a satellite is elliptical, its plane of rotation passes through the centre of earth. Reason: According to law of conservation of angular momentum plane of rotation of satellite always remin same.A. If both assertion and reason are true and the reason is the correct explanation of the assertion.B. If both assertion and reason are true but reason is not the correct explanation of the assertion.C. If assertion is true but reason is false.D. If the assertion and reason both are false.
Assertion : A planet moves faster, when it is closer to the sun in its orbit and vice versa. Reason : Orbital velocity in orbital of planet is constant.A. If both assertion and reason are true and the reason is the correct explanation of the assertion.B. If both assertion and reason are true but reason is not the correct explanation of the assertion.C. If assertion is true but reason is false.D. If the assertion and reason both are false.
The distance between centre of the earth and moon is 384000 km . If the mass of the earth is `6xx10^(24) kg` and `G=6.66xx10^(-11)Nm^(2)//kg^(2)`. The speed of the moon is nearlyA. 1 km/sB. 4 km/sC. 8 km/sD. 11.2 km/s
A stone is released from an elevator going up with an acceleration a, the acceleration of the stone after release A) a upwards B) (g – A) upwardsC) (g – A) downwardsD) g downwards
A planet in a distant solar systyem is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is `11kms^(-1)`, the escape velocity from the surface of the planet would beA. 110km/sB. 11km/sC. `1.1km//s`D. `0.11km//s`
A planet in a distant solar systyem is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is `11kms^(-1)`, the escape velocity from the surface of the planet would be
A star 2.5 times the mass of the sun and collapsed to a size of 42 km rotates with a speed of 1.2 rev. per second. (Extremely compact stars of this kind are known as neutron stars. Certain stellar objects called pulsars belong to this category). Will an object placed on its equator remain stuck to its surface due to gravity? (mass of the sun = 2 × 1030 kg).
A star 2.5 times the mass of the Sun and collapsed to a size of 12 km rotates with a speed of 1.2 rev. per second. (Extremely compact stars of this kind are known as neutrons stars. Certain observed stellar objects called pulsars are believed to belong to this category). Will an object placed on its equator emain stuck to its surface due to gravity? (mass of the Sun 2 x 1030 kg)