A satellite of mass is revolving around Earth in a circular orbit at a height of from the Earth's surface. The angular momentum of the satellite is . The value of is:
Official Solution
Correct Option: (1)
Step 1: Orbital radius
Given:
Step 2: Orbital velocity using gravitational and centripetal force balance
For circular motion, gravitational force provides the centripetal force: Simplifying, we get:
Step 3: Angular momentum of the satellite
The angular momentum of the satellite is:
Step 4: Substituting given values
Satellite mass: Orbital radius: Orbital speed:
Step 5: Substitute into the formula for angular momentum
Simplify:
Step 6: Simplifying the square root
Therefore,
Step 7: Alternative given form of angular momentum
It is given that:
Step 8: Equating both expressions
Cancel and (since both are non-zero):
Step 9: Squaring both sides
Final Answer:
Concept :
Gravitational force acts as the centripetal force for orbital motion.
Orbital velocity for a circular orbit: .
Angular momentum of a satellite: .
Simplify carefully when combining constants under square roots.
02
PYQ 2026
medium
physicsID: jee-main
A planet is moving around a star of mass in an orbit of radius . Another planet is moving around another star of mass in an orbit of radius . The ratio of time periods of revolution of and is:
1
2
3
4
Official Solution
Correct Option: (2)
Concept: According to Kepler’s third law, where is the time period, is orbital radius and is the mass of the central body. Step 1:Write the proportional relation} Step 2:Compute ratio} For : For : Step 3:Take the ratio} Thus
03
PYQ 2026
medium
physicsID: jee-main
If the string connecting and the ground is cut, find the speed with which the block hits the ground as shown.
1
3 m/s
2
4 m/s
3
m/s
4
m/s
Official Solution
Correct Option: (3)
Step 1: Apply conservation of energy. In this system, the potential energy of the block of mass is converted into the kinetic energy of both blocks after the string is cut. Step 2: Set up the energy equation. The initial potential energy is , where is the height. The final kinetic energy is the sum of the kinetic energies of both blocks: Using the relation that both blocks move together for the instant after the string is cut, we find the speed of the block just before it hits the ground is m/s. Final Answer:
