Advertisements
Advertisements
प्रश्न
Find the height over the Earth's surface at which the weight of a body becomes half of its value at the surface.
उत्तर
Assume that at height h, the weight of the body becomes half.
Weight of the body at the surface = mg
Weight of the body at height h above the Earth's surface = mg', where g' is the acceleration due to gravity at height h
\[\text { Now }, g' = \frac{1}{2}g\]
\[\therefore \left( \frac{1}{2} \right) \frac{GM}{R^2} = \frac{GM}{\left( R + h \right)^2} \left[ \because g = \frac{GM}{R^2} \right]\]
\[ \Rightarrow 2 R^2 = \left( R + h \right)^2 \]
\[ \Rightarrow \sqrt{2}R = R + h\]
\[ \Rightarrow h = \left( \sqrt{2} - 1 \right)R\]
APPEARS IN
संबंधित प्रश्न
The acceleration of moon with respect to earth is 0⋅0027 m s−2 and the acceleration of an apple falling on earth' surface is about 10 m s−2. Assume that the radius of the moon is one fourth of the earth's radius. If the moon is stopped for an instant and then released, it will fall towards the earth. The initial acceleration of the moon towards the earth will be
The acceleration of the moon just before it strikes the earth in the previous question is
If the acceleration due to gravity at the surface of the earth is g, the work done in slowly lifting a body of mass m from the earth's surface to a height R equal to the radius of the earth is
Find the acceleration due to gravity of the moon at a point 1000 km above the moon's surface. The mass of the moon is 7.4 × 1022 kg and its radius is 1740 km.
What is the acceleration due to gravity on the top of Mount Everest? Mount Everest is the highest mountain peak of the world at the height of 8848 m. The value at sea level is 9.80 m s−2.
A body is weighed by a spring balance to be 1.000 kg at the North Pole. How much will it weigh at the equator? Account for the earth's rotation only.
A particle is fired vertically upward with a speed of 15 km s−1. With what speed will it move in interstellar space. Assume only earth's gravitational field.
A mass of 6 × 1024 kg (equal to the mass of the earth) is to be compressed in a sphere in such a way that the escape velocity from its surface is 3 × 108 m s−1. What should be the radius of the sphere?
Explain the variation of g with altitude.
Calculate the change in g value in your district of Tamil nadu. (Hint: Get the latitude of your district of Tamil nadu from Google). What is the difference in g values at Chennai and Kanyakumari?
If both the mass and the radius of the earth decrease by 1%, then the value of acceleration due to gravity will
One can easily weigh the earth by calculating the mass of the earth by using the formula:
Which of the following options are correct?
- Acceleration due to gravity decreases with increasing altitude.
- Acceleration due to gravity increases with increasing depth (assume the earth to be a sphere of uniform density).
- Acceleration due to gravity increases with increasing latitude.
- Acceleration due to gravity is independent of the mass of the earth.
A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other objects in the sky and take acceleration due to gravity on the surface of the Earth and Mars as 10 m/s2 and 4 m/s2 respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time.
A pebble is thrown vertically upwards from the bridge with an initial velocity of 4.9 m/s. It strikes the water after 2 s. If acceleration due to gravity is 9.8 m/s2. The height of the bridge and velocity with which the pebble strikes the water will respectively be ______.
