Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
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
Young's modulus of elasticity $Y$ is expressed in terms of three derived quantities, namely, the gravitational constant $G$, Planck's constant $h$ and the speed of light $c$, as $Y=c^\alpha h^\beta G^\gamma$. Which of the following is the correct option?
$1$ joule of energy is to be converted into new system of units in which length is measured in $10$ metre, mass in $10 \,kg$ and time in $1$ minute. The numerical value of $1 \,J$ in the new system is
A student performs an experiment to determine the Young's modulus of a wire, exactly $2 \mathrm{~m}$ long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $0.8 \mathrm{~mm}$ with an uncertainty of $\pm 0.05 \mathrm{~mm}$ at a load of exactly $1.0 \mathrm{~kg}$. The student also measures the diameter of the wire to be $0.4 \mathrm{~mm}$ with an uncertainty of $\pm 0.01 \mathrm{~mm}$. Take $g=9.8 \mathrm{~m} / \mathrm{s}^2$ (exact). The Young's modulus obtained from the reading is
Diagrams show readings of a screw gauge. figure $(i)$ shows the zero error reading when the screw gauge is closed, figure $(ii)$ the reading when the screw gauge is being used to measure the diameter of a ball-bearing. What is the diameter of the ball-bearing in $mm$? There are $50$ divisions on circular scale