Force, Work, Energy and Power Test - 4

Let,

Initial height before drop \(\left(h_{1}\right)=20 {~m}\)

Final after bounce \(\left(h_{2}\right)=10 {~m}\)

The potential energy of the ball before drop \(\left(P_{1}\right)\) \(=m g h_{1}=20 ~m g\)

The potential energy of the ball after bounce \(\left(P_{2}\right)\) \(=m g h_{2}=10~ m g\)

As the ball is falling, its potential energy will decrease continuously until it reaches the ground and then it will start increasing after the bounce.

So the potential energy after dropping will be the fraction of initial potential energy.

The loss of energy is given by:

\(\Delta P \times 100=\frac{P_{1}-P_{2}}{P_{1}} \times 100\)

\(\Rightarrow \Delta P=\frac{20 m g-10 m g}{20 m g} \times 100\)

\(\Rightarrow \Delta P=50 \%\)

Hence, the correct option is (C).

Kinetic energy is the energy possessed by a moving object. Kinetic energy is expressed as:

\(K E=\frac{1}{2} m v^{2}\)

Where \(m\) is the mass of the object and \(v\) is the velocity of the object.

The amount of work required to stop the truck will be equivalent to the kinetic energy possessed by the truck at that moment.

Work and energy have the same unit i.e., joule and can be equated.

Let \(m\) be the mass of the car and \(v\) its velocity.

\(KE\) of the car \(=\frac{1}{2} m v^{2}\)

Let \({m}\)' and \(v\)' be the mass and velocity of the truck respectively.

Given that:

\({m}^{\prime}=8 {~m}\) and \(v^{\prime}=\frac{1}{2} v\)

\({KE}\) of the truck \(=\frac{1}{2} m^{\prime} v^{\prime 2}=\frac{1}{2}(8 m)\left(\frac{v}{2}\right)^{2}=2 \times \frac{1}{2} m v^{2}=2 \times {KE}\) of the car

Therefore, the amount of work done required to stop the truck is two times more.

Hence, the correct option is (B).

Power expended by girl:

Weight of the girl, \(\mathrm{mg}=400 \mathrm{~N}\)

Displacement (height), \(h=8 \mathrm{~m}\)

Time taken, \(\mathrm{t}=20 \mathrm{~s}\)

Total amount of Power expended,

\(P=\frac{\text { Work done }}{\text { time taken }} \)

\(=\frac{m g h}{t}\)

\(=400 \mathrm{~N} \times \frac{8 \mathrm{~m}}{20 \mathrm{~s}}\)

\(=160 \mathrm{~W}\)

Hence, the correct option is (B).

Everybody attracts another body by a force i.e force of attraction between two objects is called the force of gravitation.

• Centripetal force is the force acting towards the center of the circular path.
• Centrifugal force acts in a direction pointing away from the center of the circular path.
• Electromagnetic force: It is a type of force that occurs between electrically charged particles.

Hence, the correct option is (C).