A particle gets displaced by Δ barr=(2 hati+3 hatj+4 hatk)m under the action of a force vecF=(7 hati+4 hatj+3 hatk). The change in its kinetic energy is

Question

A particle gets displaced by Δ barr=(2 hati+3 hatj+4 hatk)m under the action of a force vecF=(7 hati+4 hatj+3 hatk). The change in its kinetic energy is (A) 38 J (B) 70 J (C) 52.5 J (D) 1.26 J

Tardigrade Admin · Accepted Answer

According to work-energy theorem, Change in kinetic energy = work done =F.Δ vecr=(7 hati+4 hatj+3 hatk)⋅(2 hati+3 hatj+4 hatk) = 14+ 12+12 = 38 J

Q. A particle gets displaced by
$Δ \overset{r}{ˉ} = (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) m$ under the action of a force
$F = (7 \hat{i} + 4 \hat{j} + 3 \hat{k}) .$ The change in its kinetic energy is

$38 J$

$70 J$

$52.5 J$

$1.26 J$

According to work-energy theorem, Change in kinetic energy = work done
$= F .Δ r = (7 \hat{i} + 4 \hat{j} + 3 \hat{k}) \cdot (2 \hat{i} + 3 \hat{j} + 4 \hat{k})$
$= 14 + 12 + 12 = 38 J$

Q. A particle gets displaced by Δrˉ=(2i^+3j^​+4k^)m under the action of a force F=(7i^+4j^​+3k^). The change in its kinetic energy is

38J

70J

52.5J

1.26J