Show that if a rod held at angle `theta` to the horizontal and released, its lower end will not slip if the friction coefficient between rod and ground is greater than `(3sinthetacostheta)/(1+3sin^(2)theta)`

A uniform rod is held at an angle of 45^@ to the horizontal and released from rest as shown. The minimum coefficient of friction between plane and rod required so that the rod does not slip on the plane upon releases, will be

prove that- (sinthetacos^3theta+sin^3thetacostheta)/(sinthetacostheta)=1

A man with mass M has its string'.attached to one end. of a spring which can move without friction along a horizontal, overhead fixed rod. The other end of the spring is fixed to a, wall. The spring constant is k. The string is massless and inextensible and it maintains a constant angle theta with the, overhead rod, even when the man moves. There is friction, iwith coefficient mu between the man and the ground. What is, the maximum distance (in m ) that the man moving slowly can stretch the spring beyond its natural length?

A uniform rod of length L rests against a smooth roller as shown in figure. Find the friction coefficient between the ground and the lower end if the minimum angle that rod can make with the horizontal is theta .

A uniform rod of length L rests against a smooth roller as shown in Fig. Find the friction coefficient between the ground and the lower end if the minimum angle that the rod can make with the horizontal is theta .

Prove (sin^3theta+cos^3theta)/(sintheta+costheta)=1-sinthetacostheta

A rod is kept inclined at an angle theta with the horizontal A sleeve of mass m can slide on the rod. If the coefficient of friction between the rod and the sleeve is mu , for what values of horizontal acceleration a of the rod, towards left, the sleeve will not slide over the rod?

A sphere can roll without slipping on a surface inclined at an angle theta if the fiiction coefficient is more than (2/7)g sin theta Suppose the friction coefficient is (l/7)g sin theta If a sphere is released from rest on this incline then which ofthe following are possible situations:

A sphere can roll on a surface inclined at an angle theta if the friction coefficient is more than (2)/(7) g sin theta . Suppose the friction coefficient is (1)/(7) g sin theta , and a sphere is released from rest on the incline,