Find the Young's modulus of the wire whose stress-strain curve is as shown in the following figure

In the circuit shown in figure, if the point \(R\) is earthed and point \(P\) is given a potential of \(+1800 \mathrm{~V}\), then charges on \(C_2\) and \(C_3\) are respectively

A particle is executing simple harmonic motion with an instantaneous displacement \(x=A \sin ^2\left(\omega t-\frac{\pi}{4}\right)\). The time period of oscillation of the particle is

Two balls of charge \(q_1\) and \(q_2\) initially have a velocity of the same magnitude and direction. After a uniform electric field has been applied during a certain time, the direction of the velocity of the first ball changes by \(60^{\circ}\), and the velocity magnitude is reduced by half. The direction of the velocity of the second ball changes thereby by \(90^{\circ}\).
In what proportion will the velocity of the second ball change? Determine the magnitude of the charge-to-mass ratio for the second ball if it is equal to \(k_1\) for the first ball. The electrostatic interaction between the balls should be neglected.

A thin circular ring and a circular disc of equal mass are rolling without sliding. If their linear velocities are equal and the total kinetic energy of the disc is 6 J, then the total kinetic energy of the ring is

The bob of a simple pendulum of length 200 cm is released from horizontal position. If \(10 \%\) of its initial energy is lost due to air resistance, then the speed of bob at the mean position is
(Acceleration due to gravity \(=10 \mathrm{~m} \mathrm{~s}^{-2}\) )

The uniform electric field intensity between the two plates of a parallel plate capacitor is \(1 \times 103 \mathrm{Vm}^{-1}\) acting vertically upwards as shown in the figure.


The plates are sufficiently long and have separation \(2 \mathrm{~cm}\). A particle of negative charge \(1 \mu \mathrm{C}\) and mass \(2 \mathrm{~g}\) is projected at an angle \(45^{\circ}\) with the electric field from the lower plate with a velocity ' \(u\) '. The maximum velocity acquired by the particle, if it is not hit the upper plate is

The water on the surface of a lake is just about to freeze. The most likely temperature at the bottom of the lake is

The ratio of the slopes of isothermal and adiabatic curves is

If a system of circles pass through \((2,3)\) and cuts the circle \(x^2+y^2=12\) orthogonally, then the equation of the locus of the centres of that system of circles, is

If the lengths of the tangents drawn from a point \(P\) to the three circles \(x^2+y^2-4=0\), \(x^2+y^2-2 x+3 y=0\) and \(x^2+y^2+7 y-18=0\) are equal, then the coordinates of \(P\) are

If the latus rectum of a hyperbola through one focus subtends an angle \(60^{\circ}\) at the other focus, then its eccentricity is

Given, \(\triangle A B C\) such that \(A\) is \(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, B\) is \(\hat{\mathbf{i}}-3 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}\) and \(C\) is \(3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}\), then \(\triangle A B C\) is