Q 1 :    

Two satellite A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of A is 3v, the speed of B will be           [2024]

• $6v$

   

• $12v$

   

• $\frac{4}{3}v$

   

• $3v$

   

Q 2 :    

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is

(Given = Radius of geo-stationary orbit for earth is $4.2\times {10}^4$ km)          [2024]

• $1.05\times {10}^4$ km

   

• $1.4\times {10}^4$ km

   

• $1.68\times {10}^5$ km

   

• $8.4\times {10}^4$ km

   

Q 3 :    

Correct formula for height of a satellite from Earth's surface is _____.     [2024]

• ${\left(\frac{T^2{R}^{2}g}{4{\pi }^2}\right)}^{1/3}-R$

   

• ${\left(\frac{T^2{R}^{2}g}{4{\pi }^2}\right)}^{1/2}-R$

   

• ${\left(\frac{T^2{R}^2}{4{\pi }^{2}g}\right)}^{1/3}-R$

   

• ${\left(\frac{T^2{R}^{2}g}{4{\pi }^2}\right)}^{-1/3}+R$

   

Q 4 :    

A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$ from earth surface. The angular momentum of the satellite is $M\sqrt{\frac{GMR}{x}}$. The value of x is ________, where M and R are the mass and radius of earth, respectively. (G is the gravitational constant)          [2025]

Q 5 :    

A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is ___ $\times {10}^{10}\mathrm{J}$. (Mass of earth $=6\times {10}^{24}\mathrm{kg}$, Radius of earth $=6.4\times {10}^6\mathrm{m}$, Gravitational constant $=6.67\times {10}^{–11}{\mathrm{Nm}}^2{\mathrm{kg}}^{–2}$)          [2025]