A force F = Kx 2 acts on a particle at an angle of 60° with the x-axis. the work done in displacing the particle from x1 to x2 will be -

Question

A force F = Kx 2 acts on a particle at an angle of 60° with the x-axis. the work done in displacing the particle from x1 to x2 will be - (A) ( kx 2/2) (B) ( k /2)( x 22- x 12) (C) ( k /6)( x 23- x 13) (D) ( k /3)( x 23- x 13)

Tardigrade Admin · Accepted Answer

d W= kx 2 dx cos 60° ∴ WD =( k /2) ∫ limits x 1 x 2 x 2 d x =( k /6)( x 23- x 13)

Q. A force $F = K x^{2}$ acts on a particle at an angle of $6 0^{\circ}$ with the $x$ -axis. the work done in displacing the particle from $x_{1}$ to $x_{2}$ will be -

$\frac{k x ^{2}}{2}$

$\frac{k}{2} (x_{2}^{2} - x_{1}^{2})$

$\frac{k}{6} (x_{2}^{3} - x_{1}^{3})$

$\frac{k}{3} (x_{2}^{3} - x_{1}^{3})$

$d W = k x^{2} d x cos 6 0^{\circ}$
$∴ W D = \frac{k}{2} x_{1} \int x_{2} x^{2} d x = \frac{k}{6} (x_{2}^{3} - x_{1}^{3})$

Q. A force F=Kx2 acts on a particle at an angle of 60∘ with the x-axis. the work done in displacing the particle from x1​ to x2​ will be -

2kx2​

2k​(x22​−x12​)

6k​(x23​−x13​)

3k​(x23​−x13​)