Question

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

Answer 1

Correct Answer: 40

To find the force acting on the spherical body, we need to determine its acceleration. We use the equation for kinetic energy: \( KE = \frac{1}{2}mv^2 \). Here, \( KE = 10000 \, J \) and \( m = 2 \, kg \). Solving for velocity \( v \), we have:

\( 10000 = \frac{1}{2} \times 2 \times v^2 \)
\( 10000 = v^2 \)
\( v = \sqrt{10000} = 100 \, m/s \)

The velocity at the end of the 5th second is \( 100 \, m/s \). Since the body starts from rest, its initial velocity \( u = 0 \). The acceleration \( a \) can be calculated using the equation:

\( v = u + at \)
\( 100 = 0 + a \times 5 \)
\( a = \frac{100}{5} = 20 \, m/s^2 \)

Next, we use Newton's second law to find the force \( F \):

\( F = ma \)
\( F = 2 \times 20 = 40 \, N \)

The computed force \( F = 40 \, N \) fits within the given range of 40,40, confirming the solution is correct. Thus, the force acting on the body is 40 N.