Question 221:
moderateA satellite of mass $m$ is orbiting the earth (of radius $R$) at a height $h$ from its surface. The total energy of the satellite in terms of $g_0$, the value of acceleration due to gravity at the earth’s surface, is:
(2016 – II)
Total energy of a satellite is the sum of kinetic and potential energy, given by $E = -\frac{GMm}{2(R+h)}$. Substituting $GM = g_0 R^2$, we obtain $E = -\frac{mg_0 R^2}{2(R+h)}$. Thus, option D is correct.
Question 222:
moderateThe escape velocity of a body on the surface of the earth is $11.2\text{ km/s}$. If the earth’s mass increases to twice its present value and radius of the earth becomes half, the escape velocity becomes:
(1997)
Escape velocity is given by $v_e = \sqrt{\frac{2GM}{R}}$. When mass becomes $2M$ and radius becomes $R/2$, $v'_e = \sqrt{\frac{2G(2M)}{R/2}} = 2v_e$. Thus, $v'_e = 2 \times 11.2\text{ km/s} = 22.4\text{ km/s}$.
Question 223:
easyA ball is dropped from a spacecraft revolving around the earth at a height of $120\text{ km}$. What will happen to the ball?
(1996)
When a ball is dropped from a spacecraft, it possesses the same orbital velocity as the spacecraft. Therefore, it continues to move with the same speed along the original orbit.
Question 224:
easyThe escape velocity from earth is $11.2\text{ km/s}$. If a body is to be projected in a direction making an angle $45^{\circ}$ to the vertical, then the escape velocity is:
(1993)
Escape velocity is a scalar quantity and is independent of the direction or angle of projection. It depends only on the mass and radius of the planet, remaining $11.2\text{ km/s}$.
Question 225:
easyThe satellite of mass $m$ is orbiting around the earth in a circular orbit with a velocity $v$. What will be its total energy?
(1991)
Kinetic energy of the satellite is $K = \frac{1}{2}mv^2$ and potential energy is $U = -mv^2$. Total energy $E = K + U = \frac{1}{2}mv^2 - mv^2 = -\frac{1}{2}mv^2$.
Question 226:
easyFor a satellite escape velocity is $11\text{ km/s}$. If the satellite is launched at an angle of $60^{\circ}$ with the vertical, then escape velocity will be:
(1989)
The escape velocity formula depends solely on the gravitational potential and mass/radius of the body. It is independent of the angle at which the object is launched.
Question 227:
easyTwo astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will:
(2017-Delhi)
Due to universal gravitational attraction between the two astronauts, they will experience a mutual attractive force and move towards each other in space.