A force \(\vec{F} = (3xy - 5z)\hat{j} + 4z\hat{k}\) is applied on a particle. The work done by the force when the particle moves from point (0, 0, 0) to point (2, 4, 0) as shown in figure is :
Answer & explanation
Correct answer: option 4
The z-component of the force and the x-component of displacement are ineffective here.
\(dW = F_y.dy = 3xy.dy\)
\(= 6 x^4. dx\)
Integrating : \(\int_0^W dW = \int_0^2 6 x^4. dx\)
\(W = \frac{6}{5}x^5\)
\(W = \frac{6}{5}*2^5\)
\(W = \frac{192}{5}\)