Two charges $7 \mu \mathrm{c}$ and $-4 \mu \mathrm{c}$ are placed at $(-7 \mathrm{~cm}, 0,0)$ and $(7 \mathrm{~cm}, 0,0)$ respectively. Given, $\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$, the electrostatic potential energy of the charge configuration is :
Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is $P_1$. The reading of the pressure gauge falls to $P_2$ when the valve is opened. The speed of water flowing in the pipe is proportional to
The energy of a system is given as $\mathrm{E}(\mathrm{t})=\alpha^3 \mathrm{e}^{-b}$, where t is the time and $\beta=0.3 \mathrm{~s}^{-1}$. The errors in the measurement of $\alpha$ and $t$ are $1.2 \%$ and $1.6 \%$, respectively. At $t=5 \mathrm{~s}$, maximum percentage error in the energy is :
Match List - I with List - II
List - I | List - II | ||
---|---|---|---|
(A) | Permeability of free space | (I) | $\left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-2}\right]$ |
(B) | Magnetic field | (II) | $\left[\mathrm{M} \mathrm{T}^{-2} \mathrm{~A}^{-1}\right]$ |
(C) | Magnetic moment | (III) | $\left[\mathrm{M} \mathrm{L} \mathrm{T}^{-2} \mathrm{~A}^{-2}\right]$ |
(D) | Torsional constant | (IV) | $\left[\mathrm{L}^2 \mathrm{~A}\right]$ |
Choose the correct answer from the options given below :