A straight wire carrying a current of \(14\,A\) is bent into a semicircular are of radius \(2.2\,cm\) as shown in the figure. The magnetic field produced by the current at the centre \((O)\) of the arc. is \(.........\,\times 10^{-4}\, T\)

Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence.

The general displacement of a simple harmonic oscillator is \(x = A \sin \omega t\). Let \(T\) be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when \(t=\frac{T}{\beta}\). The value of \(\beta\) is \(.........\)

The coordinates of a particle with respect to origin in a given reference frame is \((1,1,1)\) meters. If a force of \(\overrightarrow{\mathrm{F}}=\hat{i}-\hat{j}+\hat{k}\) acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is ______.

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency \(10\ GHz\). What is the frequency of the microwave measured by the observer?.......\(GHz\) ( speed of light \(= 3 \times  10^8 \) \(ms^{-1}\))

The box of a pin hole camera, of length \(L\), has a hole of radius \(a\). It is assumed that when the hole is illuminated by a parallel beam of light of wavelength \(\lambda\), the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size ( say \(b_{min}\)) when

For the circuit shown, with \({R_1} = 1.0\,\Omega \), \({R_2} = 2.0\,\Omega \), \({E_1} = 2\,V\) and \({E_2} = {E_3} = 4\,V\), the potential difference between the points \(‘a’\) and \(‘b’\) is approximately (in \(V\))

Assume there are two identical simple pendulum Clocks\(-1\) is placed on the earth and Clock\(-2\) is placed on a space station located at a height \(h\) above the earth surface. Clock\(-1\) and Clock\(-2\) operate at time periods \(4\,s\) and \(6\,s\) respectively. Then the value of \(h\) is \(....km\) (consider radius of earth \(R _{ E }=6400\,km\) and \(g\) on earth \(10\,m / s ^{2}\) )

A body takes \(10\, minutes\) to cool from \(60\,^oC\) to \(50\,^oC\). The temperature of surroundings is constant at \(25\,^oC\). Then, the temperature of the body after next \(10\, minutes\) will be approximately ....... \(^oC\)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The Bohr model is applicable to hydrogen and hydrogen-like atoms only.
Reason R : The formulation of Bohr model does not include repulsive force between electrons.
In the light of the above statements, choose the correct answer from the options given below :

A block of mass \(10\, kg\) starts sliding on a surface with an initial velocity of \(9.8\, ms ^{-1}\). The coefficient of friction between the surface and bock is \(0.5\). The distance covered by the block before coming to rest is: [use \(g =9.8\, ms ^{-2}\) ].........\(m\)

A transverse wave travels on a taut steel wire with a velocity of \({v}\) when tension in it is \(2.06 \times 10^{4} \;\mathrm{N} .\) When the tension is changed to \(T\). the velocity changed to \(\frac v2\). The value of \(\mathrm{T}\) is close to

Nitrogen gas is at \(300^{\circ} C\) temperature. The temperature (in \(K\)) at which the \(rms\) speed of a \(H _{2}\), molecule would be equal to the \(rms\) speed of a nitrogen molecule, is........ (Molar mass of \(N _{2}\) gas \(28\, g\) )