$A$ particle moves along a circle of radius $\frac{20}{\pi} \; m$ with constant tangential acceleration. If the velocity of the particle is $80 \; m/s$ at the end of the second revolution after motion has begun,the tangential acceleration is:

If the unit of length and force be increased four times,then the unit of energy is

Two rods of different materials having coefficients of linear expansion $\alpha_1$ and $\alpha_2$ and Young's moduli $Y_1$ and $Y_2$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If $\alpha_1 : \alpha_2 = 2 : 3$,the thermal stress developed in the two rods is equal provided $Y_1 : Y_2$ is equal to:

$A$ metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T$ ($Y$ = Young's modulus,$\rho$ = density,$\alpha$ = coefficient of linear expansion),then the frequency of transverse vibration is proportional to:

The energy levels of a certain atom are $A, B,$ and $C$ in increasing order of energy,i.e.,$E_A < E_B < E_C$. If $\lambda_1, \lambda_2,$ and $\lambda_3$ are the wavelengths of radiation corresponding to transitions $C \to B, B \to A,$ and $C \to A$ respectively,which of the following relations is correct?

If $A$ is a square matrix of order $3$,then $|\operatorname{adj}(\operatorname{adj} A^2)|$ is equal to