Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
The acceleration due to gravity at a point at height h from the surface of the moon is given by \[g = \frac{GM}{r^2}\] ,
where M is the mass of the moon; r is the distance of point from the centre of the moon and G is universal gravitational constant.
\[\therefore g = \frac{GM}{\left( R + h \right)^2}\]
\[ \Rightarrow g = \frac{6 . 67 \times {10}^{- 11} \times 7 . 4 \times {10}^{22}}{\left( 1740 + 1000 \right)^2 \times {10}^6}\]
\[ \Rightarrow g = \frac{6 . 67 \times 7 . 4 \times {10}^{11}}{\left( 1740 + {1000}^2\times {10}^6 \right)}\]
\[ \Rightarrow g = \frac{6 . 67 \times 7 . 4 \times {10}^{11}}{2740 \times 2740 \times {10}^6}\]
\[ \Rightarrow g = 0 . 65 m/ s^2\]
APPEARS IN
संबंधित प्रश्न
Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250 N on the surface?
The acceleration of the moon just before it strikes the earth in the previous question is
Suppose, the acceleration due to gravity at the earth's surface is 10 m s−2 and at the surface of Mars it is 4⋅0 m s−2. A 60 kg passenger goes from the earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of the following figure best represents the weight (net gravitational force) of the passenger as a function of time?
Find the height over the Earth's surface at which the weight of a body becomes half of its value at the surface.
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?
If the acceleration due to gravity becomes 4 times its original value, then escape speed ____________.
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 ball is immersed in water kept in container and released. At the same time container is accelerated in horizontal direction with acceleration, `sqrt44` m/s2. Acceleration of ball w.r.t. container is ______ m/s2 (specific gravity of ball = 12/17, g = 10 m/s2)
If the radius of the earth shrinks by 2% while its mass remains the same. The acceleration due to gravity on the earth's surface will approximately ______.
The percentage decrease in the weight of a rocket, when taken to a height of 32 km above the surface of the earth will, be ______.
(Radius of earth = 6400 km)
The mass of a planet is `1/10`th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is ______.
