Two rods of different materials having coefficients of thermal expansion α_1, α₂ and Young’s modulii Y_1,Y₂ respectively are fixed between two rigid massive walls. The rods are temperature. There is no bending of the rods. If α₁:α₂₌2:3, the thermal stresses developed in the two rods are equal provided Y_1:Y₂ is equal to

(a) 2:3

(b) 1:1

(c) 3:2

(d) 4:9

Three identical balls are placed on a frictionless horizontal surface touching each other. They stick to each other because of adhesive. Another ball of same radius and mass m is placed over the void created by the three balls. Find the forces applied by the balls kept on the floor to each other if the system remains in equilibrium.

A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.

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