Section – B A spherical body of mass 2 kg starting from rest acquires a kinetic energy of 10000 J at the end of 5th second. The force acted on the body is N.

Given: Mass of the spherical body is 2 kg. It starts from rest, so u = 0. The kinetic energy at the end of 5 s is 10000 J. Find: The force acting on the body. Using kinetic energy, 12mv^2 = KE Substituting the given values, 12 2 v^2 = 10000 v^2 = 10000 v = 100 m/s Now use the equation of motion, v = u + at Since u = 0 and t = 5 s, 100 = 0 + a 5 a = 1005 = 20 m/s^2 Now the force is, F = ma = 2 20 = 40 N Therefore, the force acting on the body is 40 N.

Section – B A spherical body of mass 2 kg starting from rest acqu… — Solution | JEE Physics

NVAEasyJEE 2023Kinetic Energy & Work-Energy Theorem

Section – B

A spherical body of mass $2 \, \text{kg}$ starting from rest acquires a kinetic energy of $10000 \, \text{J}$ at the end of ** $5$ **th second. The force acted on the body is _____ $\text{N}$ .

Answer

Correct answer:40

Step-by-step solution

Standard Method

Given: Mass of the spherical body is $2 \, \text{kg}$ . It starts from rest, so $u = 0$ . The kinetic energy at the end of $5 \, \text{s}$ is $10000 \, \text{J}$ .

Find: The force acting on the body.

Using kinetic energy,

\frac{1}{2}mv^2 = \text{KE}

Substituting the given values,

\frac{1}{2} \cdot 2 \cdot v^2 = 10000

v^2 = 10000

v = 100 \, \text{m/s}

Now use the equation of motion,

v = u + at

Since $u = 0$ and $t = 5 \, \text{s}$ ,

100 = 0 + a \cdot 5

a = \frac{100}{5} = 20 \, \text{m/s}^2

Now the force is,

F = ma = 2 \cdot 20 = 40 \, \text{N}

Therefore, the force acting on the body is $40 \, \text{N}$ .

Common mistakes

Using the kinetic energy formula incorrectly as $mv^2$ instead of $\frac{1}{2}mv^2$ . This gives the wrong velocity. Always start with $\frac{1}{2}mv^2 = \text{KE}$ .
Ignoring that the body starts from rest. If $u \neq 0$ is assumed, the acceleration becomes incorrect. Use $u = 0$ exactly as stated in the question.
Directly substituting kinetic energy into force formulas without first finding velocity and acceleration. Force is obtained from $F = ma$ , so first determine $v$ from kinetic energy, then $a$ from kinematics.

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Answer

Step-by-step solution

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