The elastic limit of brass is \(379\,MPa.\) .......... \(mm\) should be the minimum diameter of a brass rod if it is to support a \(400\,N\) load without exceeding its elastic limit .

The displacement x versus time graph is shown below.

(A) The average velocity during 0 to 3 s is \(10 \mathrm{~m} / \mathrm{s}\)
(B) The average velocity during 3 to 5 s is \(0 \mathrm{~m} / \mathrm{s}\)
(C) The instantaneous velocity at \(\mathrm{t}=2 \mathrm{~s}\) is \(5 \mathrm{~m} / \mathrm{s}\)
(D) The average velocity during 5 to 7 s and instantaneous velocity at \(\mathrm{t}=6.5 \mathrm{~s}\) are equal
(E) The average velocity from \(t=0\) to \(t=9 \mathrm{~s}\) is zero
Choose the correct answer from the options given below:

In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is :

The least count of a screw guage is 0.01 mm . If the pitch is increased by \(75 \%\) and number of divisions on the circular scale is reduced by \(50 \%\), the new least count will be _____ \(\times 10^{-3} \mathrm{~mm}\)

In the given circuit, the current \((I)\) through the battery will be \(..........\,A\)

A sample contains \(10^{-2}\, kg\) each of two substances A and \(B\) with half lives \(4 \,s\) and \(8 \,s\) respectively. The ratio of then atomic weights is \(1: 2\) The ratio of the amounts of \(A\) and \(B\) after \(16 \,s\) is \(\frac{x}{100}\). the value of \(x\) is........

A force \(\mathrm{f}=\mathrm{x}^2 \mathrm{y} \hat{\mathrm{i}}+\mathrm{y}^2 \hat{\mathrm{j}}\) acts on a particle in a plane \(\mathrm{x}+\mathrm{y}=10\). The work done by this force during a displacement from \((0,0)\) to \((4 \mathrm{~m}, 2 \mathrm{~m})\) is Joule (round off to the nearest integer)

Which of the following statements is false?

The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is \(6\,V\) and the load resistance is \(R_L= 4\,k\Omega .\) The series resistance of the circuit is \(R_i = 1\,k\Omega .\) If the battery voltage \(V_B\) varies from \(8\,V\) to \(16\,V,\) what are the minimum and maximum values of the current through Zener diode?

A square loop of side \(20\, {cm}\) and resistance \(1\, \Omega\) is moved towards right with a constant speed \({v}_{0}\). The right arm of the loop is in a uniform magnetic field of \(5\, {T}\). The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value \(4\, \Omega\). What should be the value of \(v_{0}\) so that a steady current of \(2\, {mA}\) flows in the loop ?

A ring of mass \(M\) and radius \(R\) is rotating about its axis with angular velocity \(\omega \). Two identical bodies each of mass \(m\) are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be

A capacitor has capacitance \(5 \mu F\) when it's parallel plates are separated by air medium of thickness \(d\). A slab of material of dielectric constant \(1.5\) having area equal to that of plates but thickness \(\frac{ d }{2}\) is inserted between the plates. Capacitance of the capacitor in the presence of slab will be \(..........\mu F\)