Angular momentum of particle about the origin is varying as L=4√2t+8 (SI units) when it moves along a straight line y=x−4 (x,y in meters).
As we know,
τ=dLdt,L=(4√2t+8)
τ=ddt(4√2t+8)=4√2 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+C√A2+B2∣∣∣
[putting (X1,Y1)=(0,0)]
=∣∣
∣∣0−0−4√12+12∣∣
∣∣=2√2
Hence, τ=F.r⊥
4√2=F.2√2 (from (1))
⇒F=2 N