Question

The kinetic energy of a particle executing SHM is 16 J, when it is at its mean position. If the mass of the particle is 0.32 kg, then what is the maximum velocity of the particle?

• A. 5 m/s
• B. 15 m/s
• C. 10 m/s
• D. 20 m/s

Answer 1

The correct option is C 10 m/s

At the mean position, kinetic energy is maximum.
In linear SHM, at the extreme position, the velocity of the particle is minimum and its acceleration is maximum. At the mean position, the velocity of the particle is maximum and its acceleration is minimum. At mean position the KE is
$KE=\frac{1}{2}m{v}_{max}^2$
or $v_{max}^2=\frac{2KE}{m}$
(Given, KE = 16J, m=0.32kg)
$\therefore v_{max}=\sqrt{\left(\frac{2KE}{m}\right)}$ ...(i)
Putting the values in Eq. (i), we get
$v_{max}=\sqrt{\frac{2\times 16}{0.32}}=\sqrt{100}=10m/s$