A milliammeter of resistance $40 \Omega$ has a range $0-30 \mathrm{~mA}$. What will be the resistance used in series to convert it into voltmeter of range $0-15 \mathrm{~V}$ ?

A child starts running from rest along a circular track of radius $r$ with constant tangential acceleration a. After time $t$ he feels that slipping of shoes on the ground has started. The coefficient of friction between shoes and the ground is

[g = acceleration due to gravity]

A metal rod has length, cross-sectional area and Young's modulus as $L, A$ and $Y$, respectively. If the elongation in the rod produced is I, then work done is proportional to

Two cells having unknown emfs $E_1$ and $E_2$ $\left(E_1>E_2\right)$ are connected in potentiometer circuit, so as to assist each other. The null point obtained is at 490 cm from the higher potential end. When cell $E_2$ is connected, so as to oppose cell $E_1$, the null point is obtained at 90 cm from the same end. The ratio of the emfs of two cells $\left(\frac{E_1}{E_2}\right)$ is