The loudness and pitch of a sound note depend on

A square wire of each side l carries a current \(I\). The magnetic field at the mid-point of the square

Rainbow is formed due to

Two point masses 1 kg and 4 kg are separated by a distance of 10 cm . The gravitational potential energy of the two point masses is

A circular coil of radius \(0.1 \mathrm{~m}\) is placed in the \(\mathrm{X}-\mathrm{Y}\) plane and a current \(2 \mathrm{~A}\) is passed through the coil in the clockwise direction when looking from above. Find the magnetic dipole moment of the current loop

The Poisson's ratio of a material is \(0.1\). If the longitudinal strain of a rod of this material is \(10^{-3}\), then the percentage change in the volume of the rod will be

A string vibrates with a frequency of \(200 \mathrm{~Hz}\). When its length is doubled and tension is altered, it begins to vibrate with a frequency of \(300 \mathrm{~Hz}\). The ratio of the new tension to the original tension is

A hockey player hits the ball at an angle of \(37^{\circ}\) from the horizontal with an initial speed of \(40 \mathrm{~m} / \mathrm{s}\) (a right angled triangle with one of the angle is \(37^{\circ}\) and their sides in the ratio of \(6: 8: 10\)). Assume that the ball is in a vertical plane. The time at which the ball reaches the highest point of its path is

Maximize \(Z=7 x_{1}-3 x_{2}\) subject to, \(x_{1}+2 x_{2} \leq 2,2 x_{1}+4 x_{2} \geq 8, x_{1} \geq 0, x_{2} \geq 0\).

From the given aqueous solutions below, arrange them in the order of their increasing boiling points.
(i) \(10^{-4} \mathrm{M} \mathrm{NaCl}\)
(ii) \(10^{-3} \mathrm{M}\) urea
(iii) \(10^{-3} \mathrm{M} \mathrm{MgCl}_2\)
(iv) \(10^{-3} \mathrm{M} \mathrm{NaCl}\)

Given below are 4 equations showing Molar conductivities at infinite dilution of various electrolytes. Which one of them represents the correct equation?
\(\begin{aligned}
& \left(\Lambda_m^0\right)_{N a B r}-\left(\Lambda_m^0\right)_{N a C l}=\left(\Lambda_m^0\right)_{\mathrm{KCl}}-\left(\Lambda_m^0\right)_{\mathrm{KBr}} \\
& \left(\Lambda_m^0\right)_{\mathrm{HCl}}+\left(\Lambda_m^0\right)_{\mathrm{KOH}}-\left(\Lambda_m^0\right)_{\mathrm{KCl}}=\left(\Lambda_m^0\right)_{\mathrm{H}_2 \mathrm{O}} \\
& \left(\Lambda_m^0\right)_{\mathrm{KBr}}-\left(\Lambda_m^0\right)_{\mathrm{NaBr}}=\left(\Lambda_m^0\right)_{\mathrm{NaBr}}-\left(\Lambda_m^0\right)_{\mathrm{Nal}} \\
& \left(\Lambda_m^0\right)_{N H_4 \mathrm{Cl}}-\left(\Lambda_m^0\right)_{\mathrm{NH}_4 \mathrm{NO}_3}=\left(\Lambda_m^0\right)_{N H_4 \mathrm{Cl}}-\left(\Lambda_m^0\right)_{N H 4 B r}
\end{aligned}\)

One end of the string of length \(l\) is connected to a particle of mass \(m\) and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed \(v\), the net force on the particle (directed towards centre) will be ( \(T\) represents the tension in the string)

Two balls are thrown horizontally, one from the window of first floor which is \(3 \mathrm{~m}\) high from the ground and second from the second floor which is \(6 \mathrm{~m}\) high from the ground, of a multi storey building, with the same speed of \(6 \mathrm{~ms}^{-1}\). Calculate the distance that will separate the two balls when they hit the ground.