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 .

Two likr paarallel forces P and Q act a given point of a body . If Q be changed to \(P^2\over{Q}\), show that the line of action of the resultant is the same as it would be if the forces were simply interchanged.

Two like parallel forces P and Q act at points A and B of a body .Their resultant meets AB in C .When the forces are interchanged , the resultant meet AB in D . if AC=DC , show that \(P:Q::2:1\)

The resultant of two like parallel forces P and Q passes through a point O .when P is incresed by R and Q by S , the resultant still passes through O and also when Q,R replaced P,Q respectively. show that

\(S={Q^2\over{P^2}}=R-{(Q-R)^2\over(P-Q)}.\)

Two unlike parallel forces P and Q (P>Q) act at A and B resp. if P and Q both increased by x show that the resultant will move through a distance \(xAB\over{P-Q}\)

P and Q are two like parallel forces . IF P be moves parallel to itself through a disance x, show that their resultant moves through a distance 

\(Px\over{P+Q}\)

P and Q are two parallel forces . Even on increasing them by x and y respec. the position of their resultant does not changed . prove that 

P:Q::x:y.

A light rod is acted upon by three parallel forces P,Q,R acting at a three point 4cm , 20cm, and 16cm repct. from one end . If the rod is in equalibrium , show that 

P:Q:R=1:3:4.

15 वीं सदी में ग्वालियर पर किस वंश के शासक का अधिकार था?

(A) कुषाण वंश

(B) तोमर वंश

(C) नाग वंश

(D) शुंग वंश

तात्या टोपे को मध्य प्रदेश के किस स्थान पर फांसी दी गई थी?

(A) शिवपुरी

(B) ग्वालियर

(C) सागर

(D) शिवनगर