First slide

Rotational motion

Question

The angular momentum of a particle about origin is varying as $L = 4 t + 8$ (SI units) when it moves along a straight line $y = x - 4$ (x,y in meters). The magnitude of force acting on the particle would be :

Difficult

A

1 N
B

2 N
C

$\sqrt{2} N$
D

$\sqrt{3} N$

Solution

$τ = \frac{d L}{d t} = 4$

y=x-4
If x=0 then y=-4
If x=4 then y=0
slope =1
From figure $r_{⊥} = 2 \sqrt{2}$
Hence $τ = r_{⊥} F$
$4 = 2 \sqrt{2} . F$ $∴ F = \sqrt{2} N$

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