Question

PHYSICS
A particle moves from position R1 = 3i + 2j - 6k to position R2 = 14i + 13j - 9k under
the action of aforce F = 8i + 2j + 6k. Find the work done by the force.
A. 50 units
D. 155 units
B. 75 units
C. 125 units
E. 200 units


answer is E.= 200 units....
please explain !!!!! ​

Answer 1

Correct Question:

A particle moves from position $\rm \overrightarrow{R}_1 = 3 \hat{i} + 2\hat{j} - 6 \hat{k}$ to position $\rm \overrightarrow{R}_2 = 14 \hat{i} + 13\hat{j} + 9 \hat{k}$ under the action of a force $\rm \overrightarrow{F} = 8 \hat{i} + 2\hat{j} + 6 \hat{k}$. Find the work done by the force.

A. 50 units

D. 155 units

B. 75 units

C. 125 units

E. 200 units

Answer:

$\boxed{\mathfrak{E. \ 100 \ J}}$

Given:

$\rm \overrightarrow{R}_1 = 3 \hat{i} + 2\hat{j} - 6 \hat{k}$

$\rm \overrightarrow{R}_2 = 14 \hat{i} + 13\hat{j} + 9 \hat{k}$

$\rm \overrightarrow{F} = 8 \hat{i} + 2\hat{j} + 6 \hat{k}$

Explanation:

Work done (W) is dot product of force vector and displacement vector i.e.

$\boxed{ \bold{ W = \overrightarrow{F}.\overrightarrow{d}}}$

So,

$\rm \implies W = \overrightarrow{F}.(\overrightarrow{R}_2 - \overrightarrow{R}_1) \\ \\ \rm \implies W = (8\hat{i} + 2\hat{j} + 6 \hat{k}).(14\hat{i} + 13\hat{j} + 9 \hat{k} - (3\hat{i} + 2\hat{j} - 6 \hat{k})) \\ \\ \rm \implies W = (8\hat{i} + 2\hat{j} + 6 \hat{k}).(14\hat{i} + 13\hat{j} + 9 \hat{k} - 3\hat{i} - 2\hat{j} + 6 \hat{k}) \\ \\ \rm \implies W = (8\hat{i} + 2\hat{j} + 6 \hat{k}).(11\hat{i} + 11\hat{j} + 15 \hat{k}) \\ \\ \rm \implies W =8 \times 11 + 2 \times 11 + 6 \times 15 \\ \\ \rm \implies W = 88 + 22 + 90 \\ \\ \rm \implies W = 200 \: J$

$\therefore$ Work done by the force = 200 J

Answer 2

Question:-

A particle moves from position

R1 = 3i + 2j - 6k to position

R2 = 14i + 13j - 9k under the action of a force F = 8i + 2j + 6k.

Find the work done by the force.

A. 50 units

D. 155 units

B. 75 units

C. 125 units

E. 200 units

Given:-

• R1 = 3i + 2j - 6k
• R2 = 14i + 13j - 9k

Answer:-

W = F . (R2 - R1)

➭ W = (8î + 2j + 6k ) . [ 14î + 13j + 9k - ( 3î + 2j - 6k)

➭ W = (8î + 2j + 6k ) . ( 14î + 13j + 9k - 3î - 2j + 6k)

➭ W = (8î + 2j + 6k ) . ( 11î + 11j + 15k)

➭ W = 8 × 11 + 2 × 11 + 6 × 15

➭ W = 88 + 22 + 90

W = 200J

Work done by the force is 200J

☞ Hence verified