a body weighs 1 kg on the surface of moon.if mass of moon is 7.4*10/\22 kg and radius of moon is 1740 km.calculate 1)force acting between body and moon2)acceleration produced in the body 3)acceleration produced in moon
Answers
Given :
Mass of the body =m=1kg
Mass of moon=M=7.4 x10 ²²kg
Radius of moon =R= 1740km=1740x1000 m
G=6.67x10⁻¹¹ N m²/kg²
According to the universal law of gravitation:
F=GMm/R²
=6.67x10 ⁻¹¹x 7.4 x10²²x 1/(1740x1000)²
=49.358x10¹¹/300276x10⁸
=1.63N
Therefore force acting on the body is 1.63N
Same force will act on the moon.
Acceleration produced on the body is :
F=ma
A=F/m
=1.63/1=1.63 m/s²
Acceleration produced on moon will be:
a’=F/M=1.63/(7.4 x10²²)
=2.2 x 10 ⁻²³ m/s²
Given,
Mass of the body, m=1kg
Mass of moon, M =7.4 x10 ²²kg
Radius of moon, R= 1740 km=1740x1000 m
Gravitational constant, G=6.67x10⁻¹¹ N m²/kg² (Standard)
Gravitational law states that:
Force, F=GMm/R²
=6.67x10 ⁻¹¹x 7.4 x10²²x 1/(1740x1000)²
=49.358x10¹¹/3027600x106
=49.358/30.276 N
=1.63 N
Therefore, Gravitational Force acting on the body and moon is 1.63N
Acceleration produced on the body is :
F=ma (Newton’s 2nd law of motion)
a=F/m
acceleration of body=1.63/1=1.63 m/s²
Let acceleration produced on moon as a’
a’=F/M=1.63/(7.4 x10²²)
acceleration of moon=2.2 x 10 ⁻²³ m/s²
