A conservative force of magnitude 100 N is directed along the line y = 3 + x is acting on a block …

Q: A conservative force of magnitude 100 N is directed along the line y = 3 + x is acting on a block of mass m = 1 kg. Find work done by the conservative force, when block displaces from A (3,1) to B (1,3).

(a) Zero

(b) 100 J

(c) 200 √2 J

(d) 400 √2 J

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Ans: (a)

Sol: given Straight line , y = x + 3

On comparing with , y = m x + c

Slope of line is , m = 1 ;

tanθ = 1 ⇒ θ = 45°

$\displaystyle \vec{F} = 100 cos45° \hat{i} + 100 sin45° \hat{j}$

$\displaystyle \vec{F} = 100 \frac{1}{\sqrt{2}} \hat{i} + 100 \frac{1}{\sqrt{2}} \hat{j}$

$\displaystyle \vec{F} = 50 \sqrt{2} \hat{i} + 50 \sqrt{2} \hat{j}$

Displacement vector , $\displaystyle \vec{s} = (1 \hat{i} + 3 \hat{j}) – (3 \hat{i} + 1 \hat{j})$

$\displaystyle \vec{s} = -2 \hat{i} + 2 \hat{j}$

$\displaystyle W = \vec{F}.\vec{s} = (50 \sqrt{2} \hat{i} + 50 \sqrt{2} \hat{j}).(-2 \hat{i} + 2 \hat{j})$

$\displaystyle \vec{F} = -100 \sqrt{2} + 100 \sqrt{2} $

W = 0