System of Parti...

The handle of a water pump is $$90$$ cm long from its piston rod. If the pivot handle is at distance of $$15$$ cm from the piston rod, calculate (a) least effort required at its other end to overcome a resistance of $$60$$ kgf and (b) mechanical of advantage of handle. 

A particle of mass m describes uniform circular motion in a horizontal plane. the quantity that is conserved is

Two blocks of masses $$10$$ kg and $$6$$ kg are connected by a spring and placed on a frictionless horizontal surface. A hammer strikes the block of mass $$10$$ kg as a result of which this block is given a velocity $$3.2$$ m/s towards the lighter block immediately on being struck. Velocity imparted to the centre of mass of their system is: 

A long, thin carpet is laid on a floor, One end of the carpet is bent back and then pulled backwards with constant unit velocity, just above the part of the carpet which is still at rest on the floor. The speed of centre of mass of the moving part is

Four identical thin rods each of mass M and length l, form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is:

A thin rod of mass $$m$$ and length $$l$$ is suspended from one of its ends. It is set into oscillation about a horizontal axis. Its angular speed is $$\omega$$ while passing through its mean position. How high will its centre of mass rise from its lowest position?

What must be the relation between length and radius of cylinder of given mass and density so that its moment of inertia about an axis through centre of mass and perpendicular to its length may be minimum

For the figure given below, the speed of centre of mass is 

The moment of inertia of a thin uniform rod of mass $$M$$ and length $$L$$ about an axis passing through its center of mass and perpendicular to length is $$I_o$$, Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is . 

Two blocks of masses 5 kg and 2 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface.An impulse provides a velocity of 7 m/s to the heavier block in the direction of the lighter block.The velocity of the centre of mass is