A spherical body of mass 2kg starting from rest acquires a kinetic of 10000 j at the end of 5th second.The force acted on the body is ____N.

JEE Mains - Work, Power & Energy

Question: A spherical body of mass \( m = 2\,\text{kg} \) starting from rest acquires a kinetic energy of \( 10000\,\text{J} \) at the end of the 5th second. The force acted on the body is ___ N.
[24-Jan-2023 Shift 1]

Select the correct answer:

(A) \(20\,\text{N}\)

(B) \(30\,\text{N}\)

(C) \(40\,\text{N}\)

(D) \(50\,\text{N}\)

Solution

Given the kinetic energy \(K = 10000\,\text{J}\) and mass \(m = 2\,\text{kg}\), we use the relation: \[ \frac{1}{2} m v^2 = 10000. \] Solving for \(v\): \[ v^2 = \frac{2 \times 10000}{2} = 10000 \quad \Longrightarrow \quad v = 100\,\text{m/s}. \]

Since the body starts from rest and reaches \(100\,\text{m/s}\) in \(t = 5\,\text{s}\), the acceleration \(a\) is: \[ a = \frac{v}{t} = \frac{100}{5} = 20\,\text{m/s}^2. \]

Finally, using Newton's second law: \[ F = m\,a = 2 \times 20 = 40\,\text{N}. \] Hence, the force acting on the body is \(40\,\text{N}\).