question_answer

A body of mass 10 kg is lying on a rough plane inclined at an angle of\[30{}^\circ \]to the horizontal and the coefficient of friction is 0.5. The minimum force required to pull the body up the plane is

A)  0.914 N          

B)  9.14 N

C)  91.4 N           

D)  914 N

Correct Answer: C

Solution :

: For motion up the plane \[P=F+mg\sin \theta \] \[=\mu R+mg\sin \theta \];\[=\mu mg\cos \theta +mg\sin \theta \] \[=mg(\mu \cos \theta +\sin \theta )\] \[=10\times 9.8(0.5\times \cos 30{}^\circ +\sin 30{}^\circ )\] \[=98(0.5\times 0.865+0.5)=98\times 0.5\times 1.865\] \[=91.385\text{ }N=91.4\text{ }N.\]