A particle experiences a variable force F = (4 x i +3 y ^ 2 j ) i… - Vidyadip

MCQ

A particle experiences a variable force $\overrightarrow{ F }=\left(4 x \hat{ i }+3 y ^{2} \hat{ j }\right)$ in a horizontal $x - y$ plane. Assume distance in meters and force is newton. If the particle moves from point $(1,2)$ to point $(2,3)$ in the $x-y$ plane, the Kinetic Energy changes by............$j$

A
$50.0$
B
$12.5$
✓
$25.0$
D
$0$

✓

Answer

Correct option: C.

$25.0$

c
$F =4 x \hat{ i }+3 y ^{2} \hat{ j }$

$WD =\Delta KE$

$W =\int \overrightarrow{ F } \cdot( dx \hat{ i }+ dy \hat{ j })$

$=\int_{1}^{2} 4 xdx +\int_{2}^{3} 3 y ^{2} dx$

$=\left(2 x ^{2}\right)_{1}^{2}+\left( y ^{3}\right)_{2}^{3}$

$=(8-2)+(27-8)$

$=6+19=25\, J$

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