# NCERT Class 11 Physics Solutions: Chapter 6 – Work, Energy, and Power Part 6

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**Question 6.11:**

A body constrained to move along the z-axis of a coordinate system is subject to a constant force given by

Where are unit vectors along the and -axis of the system respectively. What is the work done by this force in moving the body a distance of along the -axis?

**Answer:**

Force exerted on the body,

Displacement,

Work done,

Hence, of work is done by the force on the body. **Question 6.12:**

An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy and the second with. Which is faster, the electron or the proton? Obtain the ratio of their speeds. (electron mass , proton mass

**Answer:**

Electron is faster; Ratio of speeds is

Mass of the electron,

Mass of the proton,

Kinetic energy of the electron,

Kinetic energy of the proton,

For the velocity of an electron its kinetic energy is given by the relation:

For the velocity of a proton, its kinetic energy is given by the relation:

Hence, the electron is moving faster than the proton.

The ratio of their speeds:

**Question 6.13:**

A rain drop of radius falls from a height of above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until at half its original height, it attains its maximum (terminal) speed, and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey? What is the work done by the resistive force in the entire journey if its speed on reaching the ground is ?

**Answer:**

Radius of the raindrop,

Volume of the raindrop,

Density of water,

Mass of the raindrop,

Gravitational force,

The work done by the gravitational force on the drop in the first half of its journey:

This amount of work is equal to the work done by the gravitational force on the drop in the second half of its journey,

i.e.,

As per the law of conservation of energy, if no resistive force is present, then the total energy of the raindrop will remain the same.

Total energy at the top:

Due to the presence of a resistive force, the drop hits the ground with a velocity of

∴Total energy at the ground:

∴Resistive force