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In an experiment to find acceleration due to gravity $(g)$ using simple pendulum, time period of $0.5\,s$ is measured from time of $100$ oscillation with a watch of $1\;s$ resolution. If measured value of length is $10\; cm$ known to $1\; mm$ accuracy. The accuracy in the determination of $g$ is found to be $x \%$. The value of $x$ is
If time $(t)$, velocity $(u)$, and angular momentum $(I)$ are taken as the fundamental units. Then the dimension of mass $({m})$ in terms of ${t}, {u}$ and ${I}$ is
A small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta $. After some time the velocity of the ball attains a constant value known as terminal velocity ${v_T}$. The terminal velocity depends on $(i)$ the mass of the ball $m$, $(ii)$ $\eta $, $(iii)$ $r$ and $(iv)$ acceleration due to gravity $g$. Which of the following relations is dimensionally correct