Question

1. A rocket is moving up with a velocity v. If the velocity of this rocket is suddenly
tripled, what will be the ratio of two kinetic energies?

2. Avinash can run with a speed of 8 m s–1 against the frictional force of 10 N,

and Kapil can move with a speed of 3 m s–1 against the frictional force of 25 N.
Who is more powerful and why?

3. A boy is moving on a straight road against a

frictional force of 5 N. After travelling a distance
of 1.5 km he forgot the correct path at a round
about (Fig. 11.1) of radius 100 m. However,
he moves on the circular path for one and half
cycle and then he moves forward upto 2.0 km.
Calculate the work done by him.

4. Can any object have mechanical energy even if its momentum is zero?
Explain.​

Answer 1

$\large\color{purple}\underline{\underline{{ \boxed{ Answer01} }}}$

$\tt \: let \: mass \: be \: M\\ \tt \:original \: velocity = V \\ \tt \:new \: velocity = 3V\\ \\ \tt \:original \: KE = \frac{1}{2} \times M \times V^2\\ \tt \:New \: KE = \frac{1}{2} \times M \times (3 V)^2\\ \tt \:ratio= original KE / New KE\\ \\ \tt \:= ( \frac{1}{2} \times M \times \: V^2)/(\frac{1}{2} \times M \times (3V)^2)\\ \\ \tt \:= \frac{ V^2} {9 V^2}\\ \\ \tt \:= \frac{1}{9}$

$\large\color{purple}\underline{\underline{{ \boxed{ Answer02} }}}$

To find power;

$\color{green}\underline{ \underline{\underline{{ \boxed{P=Fv} }}}}$

Avinash’s power:

Avinash is moving with velocity,

$\tt \: v_A=8m/s \: against \: frictional \: force of \: 10N$

To move with a constant velocity against a force, Avinash must also apply the same amount of force in opposite direction, thus, we can say that:

$\tt \: PA=10×8PA=80W$

In Kapil’s case:

Kapil is moving with a velocity,

$\tt \: v_K=3m/s \: against \: \: frictional \: force \: of \: 25N$

This means that Kapil is also exerting the same amount of force in the opposite direction.

Hence, we can write:

$\tt \: F_K=25N$

Now, we can calculate the power of Kapil as:

$\tt { P_K=25×3PK=75W}$

We can clearly see that the power of Avinash is

more than that of Kapil.

Hence, Avinash is more powerful than Kapil.

$\large\color{purple}\underline{\underline{{ \boxed{ Answer03} }}}$

Given, force applied by boy against friction = 5 N

Displacement on the circular path = One cycle + Half cycled = 0 + Half cycle

$\tt \: = 0 + Diameter \: of \: circular \: path \\ \tt \:= 0+ 2r = 0+2×100 \: \: \: \: \: \: \: \: \: [∴r = 100m]\\ \tt \:= 0 + 200 = 200 m\\ \\ \tt \:∴ Total \: displacements = 1.5 km + 200 m + 2.0 km\\ \tt \:= 1.5 x 1000 + 200 + 2 \times 1000km\\ \tt \:= 3700 m\\ \\ \tt \:Work \: done \: by \: boy = F . s cos θ\\ \tt \:= 5 \times 3700 \times cos 0 = 18500 J$

$\large\color{purple}\underline{\underline{{ \boxed{ Answer04} }}}$

Yes, an object can have momentum even when its mechanical energy is zero because Mechanical energy is the sum of potential energy and the Kinetic energy.

$\tt \: Mechanical \: Energy \: (M.E) = Potential \: energy (P.E) + Kinetic Energy (K.E) \\ \tt \: M.E = 0 \\ \tt \:K.E + P.E = 0\\ \tt \:P.E = -K.E$

It has some kinetic energy. It means that the body has motion.

Hence,Even if its mechanical energy is zero, the body has momentum.

Additional Information for this answer:

• Conservation of energy, according to which the energy of interaction of body or particles in a closed system is constant.
• Momentum is mass in motion, and any moving object can have momentum.
• The change in the momentum of an object is equal to its momentum. The momentum is not equal to the momentum itself rather, it is an increase or decrease in the amount of motion of an object.

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