A particle is moved from (.0,0.) to (.a,a.) under a force F=(.3 hati+4 hatj.) from two paths. Path 1 is OP and work done by force is W1 and Path 2 is OQP and work done by the force in this path is W2 . Select the correct relation between W1 and W2 .

Question

A particle is moved from (.0,0.) to (.a,a.) under a force F=(.3 hati+4 hatj.) from two paths. Path 1 is OP and work done by force is W1 and Path 2 is OQP and work done by the force in this path is W2 . Select the correct relation between W1 and W2 . <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-fqzaiwbt7lgn27l7.jpg" /> (A) W1=W2 (B) W1=2W2 (C) W2=2W1 (D) W2=4W1

Tardigrade Admin · Accepted Answer

The force is constant and hence conservative.
For conservative forces, work done is independant of the path followed.

W = F \to . S \to

,
Displacement is same for both the paths.

∴ W_{1} = W_{2}

Q. A particle is moved from $(0, 0)$ to $(a, a)$ under a force $F = (3 \hat{i} + 4 \hat{j})$ from two paths. Path $1$ is $OP$ and work done by force is $W_{1}$ and Path $2$ is $OQP$ and work done by the force in this path is $W_{2}$ . Select the correct relation between $W_{1}$ and $W_{2}$ .

$W_{1} = W_{2}$

$W_{1} = 2 W_{2}$

$W_{2} = 2 W_{1}$

$W_{2} = 4 W_{1}$

The force is constant and hence conservative.
For conservative forces, work done is independant of the path followed.
$W = F \to . S \to$ ,
Displacement is same for both the paths.
$∴ W_{1} = W_{2}$

Q. A particle is moved from (0,0) to (a,a) under a force F=(3i^+4j^​) from two paths. Path 1 is OP and work done by force is W1​ and Path 2 is OQP and work done by the force in this path is W2​ . Select the correct relation between W1​ and W2​ .

W1​=W2​

W1​=2W2​

W2​=2W1​

W2​=4W1​