Question

A variable force, given by the $2-dimensional$ vector $\overrightarrow{F}=(3x^2\hat{i}+4\hat{j})$, acts on a particle. The force is in newton and $x$ is in metre. What is the change in the kinetic energy of the particles as its moves from the point with coordinates $(2,3)$ to $(3,0)$? The coordinates are in metres.)

• A. $-7J$
• B. Zero
• C. $+7J$
• D. $+19J$

Answer 1

Answer: (C)

$+7J$

We know, Work Done $=\overrightarrow{F}.\overrightarrow{S}$

Here, $dw=\int Fds$

$\Rightarrow W=$ ${\int }_2^{3}3x^{2}dx$ $+{\int }_3^{0}4dy$

$=$ $3{\int }_2^3{x}^{2}dx$ $+4{\int }_3^{0}dy$

$=[x^3{]}_2^3+4[y{]}_3^0$

$=[x^3{]}_2^3+4[y{]}_3^0$

$=[3^3-2^3]+4[0-3]$

$=+7J$

since work done is equal to the change in kinetic energy, option C is correct.