A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is $8 \mathrm{~m} / \mathrm{s}$. The speed of the particle on the rim of the wheel at the same level as the centre of wheel, will be :

In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of $\left[\mathrm{M}^{\mathrm{P}} \mathrm{L}^{\mathrm{Q}} \mathrm{T}^R A^{\mathrm{S}}\right]$. The value of P and Q are :

The displacement x versus time graph is shown below.

(A) The average velocity during 0 to 3 s is $10 \mathrm{~m} / \mathrm{s}$

(B) The average velocity during 3 to 5 s is $0 \mathrm{~m} / \mathrm{s}$

(C) The instantaneous velocity at $\mathrm{t}=2 \mathrm{~s}$ is $5 \mathrm{~m} / \mathrm{s}$

(D) The average velocity during 5 to 7 s and instantaneous velocity at $\mathrm{t}=6.5 \mathrm{~s}$ are equal

(E) The average velocity from $t=0$ to $t=9 \mathrm{~s}$ is zero

Choose the correct answer from the options given below :

Consider a rectangular sheet of solid material of length $l=9 \mathrm{~cm}$ and width $\mathrm{d}=4 \mathrm{~cm}$. The coefficient of linear expansion is $\alpha=3.1 \times 10^{-5} \mathrm{~K}^{-1}$ at room temperature and one atmospheric pressure. The mass of sheet $m=0.1 \mathrm{~kg}$ and the specific heat capacity $C_{\mathrm{v}}=900 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$. If the amount of heat supplied to the material is $8.1 \times 10^2 \mathrm{~J}$ then change in area of the rectangular sheet is :