Physics - NLM Question with Solution | TestHub

Because the block moves with a uniform velocity, the resultant force is zero. Resolving $F$ into horizontal component $F\cos \theta$ and vertical component $F\sin \theta$, we get
$$\begin{array}{rl}& R+F\sin \theta =mg\text{ or }R=mg-F\sin \theta \\ & \text{ Also }f=\mu R=\mu (mg-F\sin \theta )\\ & \text{ But }F\cos \theta =f\\ & \text{ or }F\cos \theta =\mu (mg-F\sin \theta )\\ & \text{ or }F(\cos \theta +\mu \sin \theta )=\mu mg\\ & \therefore F=\frac{\mu mg}{\cos \theta +\mu \sin \theta }\end{array}$$ Work $W=Fs\cos \theta$ $$\begin{array}{rl}& \therefore W=\frac{\mu mgd\cos \theta }{\cos \theta +\mu \sin \theta }\\ & (\because s=d)\end{array}$$