First slide

Work Energy Theorem

Question

A particle moves 3m along the straight line $x - y + 8 = 0$ with constant speed under the influence of a constant force $\vec{F} = (a \hat{i} - 3 \hat{j}) N$ . Then the value of ‘a’ is

Moderate

A

3
B

5
C

4
D

2

Solution

$x - y + 8 = 0 \Rightarrow y = x + 8$ . So the angle between the straight line and positive x-axis is 45^o.
$∴$ Displacement $\vec{d} = (3 \cos 45^{o} \hat{i} + 3 \sin 45^{o} \hat{j}) m$
$\Rightarrow \vec{d} = \frac{3}{\sqrt{2}} (\hat{i} + \hat{j}) m$
Since the speed remains constant, change in kinetic energy is zero, hence work done by the force is zero.
$∴ \vec{F} . \vec{d} = 0 \Rightarrow (a \hat{i} - 3 \vec{j}) . \frac{3}{\sqrt{2}} (\hat{i} + \hat{j}) = 0$
$\Rightarrow a - 3 = 0 \Rightarrow a = 3$

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