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Question

The angular momentum of a particle about the origin is varying as L=42t+8 (SI units) when it moves along a straight liney=x4 (x,y in meters). The magnitude of force (in N) acting on the particle would be

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Solution

Angular momentum of particle about the origin is varying as L=42t+8 (SI units) when it moves along a straight line y=x4 (x,y in meters).
As we know,
τ=dLdt,L=(42t+8)
τ=ddt(42t+8)=42 Nm(1)
and τ=|r×F|=rF.sinθ
τ=F.(rsinθ)=F.r
where r is the perpendicular distance of force vector from origin.
Force is acting along a straight line. Hence, the perpendicular distance of the line from origin is given as
r=AX1+BY1+CA2+B2
[putting (X1,Y1)=(0,0)]
=∣ ∣00412+12∣ ∣=22
Hence, τ=F.r
42=F.22 (from (1))
F=2 N

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