A brass disc fits simply in a hole of a steel plate. The disc from the hole can be loosened if the system

A steel tape is calibrated at $20^{\circ} C$. On a cold day when the temperature is $-15^{\circ} C$, percentage error in the tape will be ……….. $\%$ $\left[\alpha_{\text {steel }}=1.2 \times 10^{-5}{ }^{\circ} C ^{-1}\right]$

Two rods of different materials having coefficient of linear expansion $\alpha_1$and $\alpha_2$ and  Young's modulii $Y_1$ 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 two rods are equal provided $Y_1 : Y_2$ is equal to

A bimetallic strip is formed out of two identical strips, one of copper and other of brass. The coefficients of linear expansion of the two metals are ${\alpha _C}$ and ${\alpha _{B}}.$ On heating, the temperature of the strip goes up by $\Delta T$ and the strip bends to form an arc of radius of curvature $R.$ Then $R$ is

The coefficients of thermal expansion of steel and a metal $X$ are respectively $12 × 10^{-6}$ and $2 × 10^{-6} per^o C$. At $40^o C$, the side of a cube of metal $X$ was measured using a steel vernier callipers. The reading was $100 \,\,mm$.Assuming that the calibration of the vernier was done at $0^o C$, then the actual length of the side of the cube at $0^o C$ will be