Two forces \(P\over{\sqrt2}\) and Q acting parallel to length and base of a smooth inclinded plaine respectively. would each of them singly support a Weight W on the plane . Prove that that \(P^2 \)is the harmonic mean between \(Q^2 and W^2\).

A force P when applied along the smooth inclinded plane support a Weight \(W_1\) and when applied horizontally balances a weight \(W_2\) on the same plane . Prove that \(P^2=W_1^2-W_2^2.\)

Show that the smallest force which will keep a body in equilibrium on a smooth inclined plane must act along the plane.

A horizontal force of 15 kg . wt. can supported a weight 20 kg. on a smooth inclinded plane . When force acting parallel to the plane will supported the same weight.

A particle of weight 50 kg . is placed on smooth surface  inclinded to the horizontal at an angle \(sin^{-1}{3\over5}.\)Find the magnitude of the force 

1) Acting parallel to the plane 

2) acting horizontally, required to keep the body in equalibrium.

A body is sustained on a smooth plane by forces each equal to half of its weight , one acting horizontally and the other along the plane . Find the inclination of the plane.

Two  parallel force of magnitude 12N and 8N act at two points 45cm apart on a rigid body . Find the magnitude , direction  and the position of application of their resultant when the force are 

1) like 

2) unlike

The resultant of two parallel forces whose  line of action are 12 m apart  and act in opposite sense is 700 N. if the resultant act at 3m from the forces , what are the forces ?

The resultant of two like parallel forces P and Q acting at point A and B aparts , 40 N . If the resultant passes through C,  where AC=3cm , Find the magitude of the forces .Also  show that if the forces where interchanged , the resultant  shifts through a distance of 2cm.

If the position of the resultant of two like paraallel forces remains unaltered when their positions are interchanged , show that the froces are equal.

A light rod ,12 cms long is suspended in a horizontal position by mean of two verticle strings. One string can stand a tension of 10gms and other of 20gms . a ring weighing 25gms can slide along the rod. find the least distance of the ring fromthe string .