physics ncert exemplar solutions class 12th chapter two

A slab of dielectric constant K has the same cross-sectional area as the plates of a parallel plate capacitor and thickness $\frac{3}{4}d,$ where d is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be:

(Given C₀ = capacitance of capacitor with air as medium between plates.)

Dimensional formula for thermal conductivity is (here $K$ denotes the temperature):

A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm^-2 . The density of water is 1 gmcm^-3 and water offers negligible drag force on the bubble. The mass of the bubble is: (g=980 cm/s²)

Particle $A$ of mass $m_A=\frac{m}{2}$ moving along the $x$ -axis with velocity $v_0$ collides elastically with another particle $B$ at rest having mass $m_B=\frac{m}{3}$ . If both particles move along the $x$ axis after the collision, the change $\mathrm{\Delta }\lambda$ in de-Broglie wavelength of particle $A$ , in terms of its de-Broglie wavelength $\left({\lambda }_0\right)$ before collision is:

In an experiment of find out diameter of wire using screw gauge, the following observations were noted:

(A) Screw moves 0.5mm on main scale in one complete rotation

(B) Total divisions on circular scale = 50

(C) Main scale reading is 2.5 mm

(D) 45th division of circular scale is in the pitch line

(E) Instrument has 0.03 mm negative error

Then the diameter of wire is:

A traveling microscope has 20 divisions per cm on the main scale while its vernier scale has total 50 divisions and 25 vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope?

Given below are two statements: One is labeled as Assertion (A) and other is labeler as Reason (R).

Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is $\rho$ and radius of the drop is r, then

$T=K\sqrt[]{\raisebox{1ex}{$\rho r^3$}\!\left/ \!\raisebox{-1ex}{$S^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$}\right.}$ is dimensionally correct, where K is dimensionless.

Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period.

In the light of above statements, choose the correct answer from the options given below.

Given below are two statements: One is labeled as Assertion (A) and other is labeler as Reason (R).

Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is  and radius of the drop is r, then

$T=K\sqrt[]{\raisebox{1ex}{$\rho r^3$}\!\left/ \!\raisebox{-1ex}{$S^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$}\right.}$  is dimensionally correct, where K is dimensionless.

Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period.

In the light of above statements, choose the correct answer from the options given below.

A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is $\frac{x}{15}\frac{{\in }_{0}A}{b},$  the value of x is……………

A quantity $X$ is given by $\left({\mathrm{I}\mathrm{F}\mathrm{v}}^2\mathrm{M}\mathrm{L}{\mathrm{L}}^4\right)$ in terms of moment of inertia $\mathrm{I}$ , force $\mathrm{F}$ , velocity $\mathrm{v}$ , work $W$ and Length $L$ . The dimensional formula for $x$  is same as that of: