A small particle moves to position 5 hati-2 hatj+ hatk from its initial position 2 hati+3 hatj-4 hatk under the action of force 5 hati+2 hatj+7 hatk N. The value of work done will be J.

Question

A small particle moves to position 5 hati-2 hatj+ hatk from its initial position 2 hati+3 hatj-4 hatk under the action of force 5 hati+2 hatj+7 hatk N. The value of work done will be J. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

W= vecF ⋅( vecrf- vecr i ) =(5 hati+2 hatj+7 hatk) ⋅((5 hati-2 hatj+ hatk)-(2 hati+3 hatj-4 hatk)) W=40 J

Q. A small particle moves to position $5 \hat{i} - 2 \hat{j} + \hat{k}$ from its initial position $2 \hat{i} + 3 \hat{j} - 4 \hat{k}$ under the action of force $5 \hat{i} + 2 \hat{j} + 7 \hat{k} N$ . The value of work done will be ________ $J$ .

$W = F \cdot (r_{f} - r_{i})$
$= (5 \hat{i} + 2 \hat{j} + 7 \hat{k}) \cdot ((5 \hat{i} - 2 \hat{j} + \hat{k}) - (2 \hat{i} + 3 \hat{j} - 4 \hat{k}))$
$W = 40 J$

Q. A small particle moves to position 5i^−2j^​+k^ from its initial position 2i^+3j^​−4k^ under the action of force 5i^+2j^​+7k^N. The value of work done will be ________J.

W=F⋅(rf​−ri​) =(5i^+2j^​+7k^)⋅((5i^−2j^​+k^)−(2i^+3j^​−4k^)) W=40J

Q. A small particle moves to position $5 \hat{i} - 2 \hat{j} + \hat{k}$ from its initial position $2 \hat{i} + 3 \hat{j} - 4 \hat{k}$ under the action of force $5 \hat{i} + 2 \hat{j} + 7 \hat{k} N$ . The value of work done will be ________ $J$ .

$W = F \cdot (r_{f} - r_{i})$
$= (5 \hat{i} + 2 \hat{j} + 7 \hat{k}) \cdot ((5 \hat{i} - 2 \hat{j} + \hat{k}) - (2 \hat{i} + 3 \hat{j} - 4 \hat{k}))$
$W = 40 J$