An ice block at `0^(@)C` is dropped from height `'h'` above the ground. What should be the value of `'h'` so that it melts completely by the time it reaches the bottom assuming the loss of whole gravitational potential energy is uded as heat by the ice? `[Given: L_(f) = 80 cal//gm]`

10 g of ice at 0^(@)C is mixed with m mass of water at 50^(@)C . What is minimum value of m so that ice melts completely. (L = 80 cal/g and s = 1 cal/ g-.^(@)C )

A rock is dropped from rest from a height h above the ground. It falls and hits the ground with a speed of 11 m/s. From what height should the rock be dropped so that its speed on hitting the ground is 22 m/s ? Neglect air resistance.

An ice block at 0^(@)C and of mass m is dropped from height 'h' such that the loss in gravitational potential energy of block is exactly equal to the heat required to just completely melt the ice. Taking latent heat of fusion of ice = 80 cal//gm , acceleration due to gravity = 10 m//s^(2) and mechanical equivalent of heat = 4.2 J//Cal . the value of 'h' is

A particle of mass m is dropped from a height h above the ground. Simultaneously another particle of the same mass is thrown vertically upwards from the ground with a speed of sqrt(2gh) . If they collide head-on completely inelastically, then the time taken for the combined mass to reach the ground is

From what height must a block of ice be dropped in order that it may melt completely. It is assumed that the whole of energy is retained by ice. Given that latent heat of ice = 80 cal g^(-1) .

Two cylinders of equal masses, one made of material A and the other of material B, are heated to 50^(@) C and placed on two large blocks of ice at 0^(@) C If both the cylinders have the same height, find the ratio (h_(A)//h_(B)) of their maximum depth of penetration in the ice. Assume that no heat is lost to the surroundings and change in gravitational potential energy is not considered S_(A)=0.2cal g^(-1)(C^(@)),rho_(A) = 4 g cm^(-3) S_(B) = 0.1 cal g^(-1) (C^(@)), rho_(B)=2 g cm^(-3)

A particle of mass m is dropped from a height h above the ground. At the same time another particle of mass 2m is thrown vertically upwards from the ground with a speed of sqrt(gh) . If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of sqrt(h/g) is :

A block of ice with an area A and a height h floats in water of density rho_(0) . What work should be performed to submerge the ice block completely into water if density of ice is rho_(1) ?

A lead ball at 30^(@)C is dropped from a height h. The ball is heated due to the air resistance and it completely melts just before reaching the ground, The molten substance falls slowly on the ground. Latent heat of fusion of lead is 22200 Jk//g . Specific heat capacity of lead =126J//kg-^(@)C and melting point of lead =330^(@)C , Assume that all mechanical energy lost is used to heat the ball. Find the value of h in km ? ("Use" g=10 m//s2)