A block of mass \(5\,kg\) is placed at rest on a table of rough surface. Now, if a force of \(30\,N\) is applied in the direction parallel to surface of the table, the block slides through a distance of \(50\,m\) in an interval of time \(10\,s\). Coefficient of kinetic friction is (given, \(g =10\,ms ^{-2}\))

An object is placed at a distance of \(12 \,{cm}\) from a convex lens. A convex mirror of focal length \(15 \,{cm}\) is placed on other side of lens at \(8 \,{cm}\) as shown in the figure. Image of object coincides with the object.When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be ..... \((cm)\)

For a plane electromagnetic wave, the magnetic field at a point \(x\) and time \(t\) is \(\overrightarrow{ B }( x , t )=\left[1.2 \times 10^{-7} \sin \left(0.5 \times 10^{3} x +1.5 \times 10^{11} t \right) \hat{ k }\right] T\) The instantaneous electric field \(\overrightarrow{ E }\) corresponding to \(\overrightarrow{ B }\) is : (speed of light \(\left.c=3 \times 10^{8} ms ^{-1}\right)\)

A hoop of radius \(r\) and mass \(m\) rotating with an angular velocity \(\omega_0\) is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density \(+\sigma\) and \(-2 \sigma\). The force experienced by a point charge +q placed at the mid point between two plates will be :

The figure given below shows an \(LCR\) series circuit with two switches \(S_1\) and \(S_2\). When switch \(S_1\) is closed keeping \(S_2\) open, the phase difference \((\phi)\) between the current and source voltage is \(30°\) and phase difference is \(60°\) when \(S_2\) is closed keeping \(S_1\) open. The value of \((3L_1 - L_2)\) is _______ H.

In an experiment of single slit diffraction pattern, first minimum for red light coincides with first maximum of some other wavelength . If wavelength of red light is \(6600\,\mathop A\limits^o\) , then wavelength of first maximum will be.....\(\mathop A\limits^o \)

A uniformly tapering conical wire is made from a material of Young's modulus \(Y\)  and has a normal, unextended length \(L.\) The radii, at the upper and lower ends of this conical wire, have values \(R\) and \(3R,\)  respectively. The upper end of the wire is fixed to a rigid support and a mass \(M\) is suspended from its lower end. The equilibrium extended length, of this wire, would equal 

Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one. Reason \(R:\) Capacitance of metallic spheres depend on the radii of spheres. In the light of the above statements, choose the correct answer from the options given below.

A plane electromagnetic wave of frequency \(50\, MHz\) travels in free space along the positive \(x-\) direction. At a particular point in space and time, \(\vec E = 6.3\,\hat j\,V/m\) . The corresponding magnetic field \(\vec B\), at that point will be

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths \(r\) =\(\frac{{{\lambda _1}}}{{{\lambda _2}}}\) is given by