For the following questions answer them individually
Given below are two statements : Statement (I) : Dimensions of specific heat is $$[L^2 T^{-2} K^{-1}]$$. Statement (II) : Dimensions of gas constant is $$[ML^2 T^{-1} K^{-1}]$$. In the light of the above statements, choose the most appropriate answer from the options given below.
A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in $$t_1$$. If it is projected vertically downwards from the same point with the same speed, it reaches the ground in $$t_2$$. Time required to reach the ground, if it is dropped from the top of the tower, is :
A body of weight $$200 \text{ N}$$ is suspended from a tree branch through a chain of mass $$10 \text{ kg}$$. The branch pulls the chain by a force equal to (if $$g = 10 \text{ m/s}^2$$) :
A car of $$800 \text{ kg}$$ is taking turn on a banked road of radius $$300 \text{ m}$$ and angle of banking $$30°$$. If coefficient of static friction is $$0.2$$ then the maximum speed with which car can negotiate the turn safely: $$(g = 10 \text{ m/s}^2, \sqrt{3} = 1.73)$$
When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be:
Assuming the earth to be a sphere of uniform mass density, a body weighed $$300 \text{ N}$$ on the surface of earth. How much it would weigh at $$R/4$$ depth under surface of earth?
Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : $$R$$ = Radius of bubble, $$S$$ = Surface tension of bubble)
A total of $$48 \text{ J}$$ heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by $$2°C$$. The work done by the gas is: Given, $$R = 8.3 \text{ J K}^{-1} \text{ mol}^{-1}$$.
Energy of 10 non rigid diatomic molecules at temperature $$T$$ is :
Two identical conducting spheres $$P$$ and $$S$$ with charge $$Q$$ on each, repel each other with a force $$16 \text{ N}$$. A third identical uncharged conducting sphere $$R$$ is successively brought in contact with the two spheres. The new force of repulsion between $$P$$ and $$S$$ is :
