A body of mass \((5 \pm 0.5) kg\) is moving with a velocity of \((20 \pm 0.4) m / s\). Its kinetic energy will be

Let \([ {\varepsilon _0} ]\) denote the dimensional formula of the permittivity of vacuum. If \(M =\) mass, \(L=\) length, \(T =\) time and \(A=\) electric current, then:

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is \(5 / x\). The value of \(x\) is _________ .

A rigid massless road of length \(3l\) has tow masses attached at each end as shown in the figure. The rod is pivoted at point \(P\) on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be

A uniform disc of radius \(R\) and mass \(M\) is free to rotate only about its axis. A string is wrapped over its rim and a body of mass \(m\) is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is

In the circuit shown, current (in \(A\)) through \(50\; V\) and \(30\; V\) batteries are, respectively

Given below are two statements :
Statement-I : A plane wave after passing through prism remains as plane wave but passing through small pin hole may become spherical wave.
Statement-II : The curvature of a spherical wave emerging from a slit will increase for increasing slit width.
In the light of the above statements, choose the correct answer from the options given below.

A force of \(F=(5 y+20) \hat{j} \,N\) acts on a particle. The work done by this force when the particle is moved from \(y=0 \,m\) to \(y=10 \,{m}\) is \(...\,{J}.\)

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 plano convex lens of refractive index \({\mu _1}\) and focal length \(f_1\) is kept in contact with another plano concave lens of refractive index \({\mu _2}\) and focal length \(f_2\). If the radius of curvature of their spherical faces is \(R\) each and \(f_1 = 2f_2\), then \({\mu _1}\) and \({\mu _2}\) are related as

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