For the following questions answer them individually
Given below are two statements:
Statement (I) : Planck's constant and angular momentum have the same dimensions.
Statement (II) : Linear momentum and moment of force have the same dimensions. In light of the above statements, choose the correct answer from the options given below :
Position of an ant (S in metres) moving in $$Y - Z$$ plane is given by $$S = 2t^2 \hat{j} + 5\hat{k}$$ (where $$t$$ is in second). The magnitude and direction of velocity of the ant at $$t = 1$$ s will be :
A train is moving with a speed of $$12 \text{ m s}^{-1}$$ on rails which are $$1.5$$ m apart. To negotiate a curve radius $$400$$ m, the height by which the outer rail should be raised with respect to the inner rail is (Given, $$g = 10 \text{ m s}^{-2}$$):
Two bodies of mass $$4$$ g and $$25$$ g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :
A body of mass $$1000$$ kg is moving horizontally with a velocity $$6 \text{ m s}^{-1}$$. If $$200$$ kg extra mass is added, the final velocity (in $$\text{m s}^{-1}$$) is:
The acceleration due to gravity on the surface of earth is $$g$$. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :
Given below are two statements :
Statement (I) : Viscosity of gases is greater than that of liquids.
Statement (II) : Surface tension of a liquid decreases due to the presence of insoluble impurities. In the light of the above statements, choose the most appropriate answer from the options given below :
$$0.08$$ kg air is heated at constant volume through $$5°C$$. The specific heat of air at constant volume is $$0.17 \text{ kcal kg}^{-1} \text{ °C}^{-1}$$ and $$1 \text{ J} = 4.18 \text{ joule cal}^{-1}$$. The change in its internal energy is approximately.
The average kinetic energy of a monatomic molecule is $$0.414$$ eV at temperature: (Use $$K_B = 1.38 \times 10^{-23} \text{ J mol}^{-1} \text{ K}^{-1}$$)
An electric charge $$10^{-6}$$ $$\mu$$C is placed at origin $$(0, 0)$$ m of $$X - Y$$ co-ordinate system. Two points $$P$$ and $$Q$$ are situated at $$(\sqrt{3}, \sqrt{3})$$ m and $$(\sqrt{6}, 0)$$ m respectively. The potential difference between the points $$P$$ and $$Q$$ will be :
