Question

Solve question in above pic with explanation​

Answer 1

Answer:

Given:

An object of mass "m" is projected from height R/2 above earth surface.

To find:

The minimum KE which will send the object to infinity.

Concept:

Whenever we talk about infinity, we mean that the potential energy of the object will be zero ( as compared to earth surface).

Again minimum KE refers to the fact that the velocity of the object upon reaching infinity will be zero.

Formulas used:

Potential energy = - (G × M × m)/d,

where G is the Gravitational constant, M is mass of earth, m is mass of object.

Potential energy denoted as PE.

Kinetic energy is denoted as KE.

Calculation:

According to conservation of energy

KE1 + PE1 = KE2 + PE2

=> KE1 - (GMm)/{R+(R/2)} = 0+0

=> KE1 - (GMm)/(3R/2) = 0

=> KE1 = 2GMm/3R.

So option 1) is correct.