koolman

A solid ball of density half that of water falls freely under gravity from a height of 19.6 m and then enter water. Upto what depth will the ball go? How much time will it take to come again to the water surface? Neglect air resistance & velocity effects in water.

Find the equations of the tangents of the parabola y^2 = 12x, which passes through the point (2,5).

Yes

A piston of mass M = 3kg and radius R = 4cm has a hole into which a thin pipe of radius r = 1cm is inserted. The piston can enter a cylinder tightly and without friction, and initially it is at the bottom of the cylinder. 750gm of water is now poured into the pipe so that the piston & pipe are lifted up as shown. Find the height H of water in the cylinder and height h of water in the pipe.

Can you tell me how

A spring of mass m is pulled such that a given instant, velocity of both of its end is v in the opposite direction. Find the kinetic energy of the spring. I tried Lets find the kinetic energy of half of the spring. Its velocity changes from zero at center to v of its end. The average velocity of half of the spring is v/2 . The kinetic energy of half of the spring is 1/2 (m/2)(v/2)^2 The kinetic energy of the spring is (m/2)(v/2)^2 Hence my ans is mv^2/8 But ans is mv^2/6