At time \(t =0\) a particle starts travelling from a height \(7\,\hat{z} cm\) in a plane keeping \(z\) coordinate constant. At any instant of time it's position along the \(x\) and \(y\) directions are defined as \(3\,t\) and \(5\,t^{3}\) respectively. At \(t =1\,s\) acceleration of the particle will be.

Regarding self-inductance:
A. The self-inductance of the coil depends on its geometry.
B. Self-inductance does not depend on the permeability of the medium.
C. Self-induced e.m.f. opposes any change in the current in a circuit.
D. Self-inductance is electromagnetic analogue of mass in mechanics.
E. Work needs to be done against self-induced e.m.f. in establishing the current.
Choose the correct answer from the options given below:

An aluminium rod with Young's modulus \(Y =7.0\) \(\times 10^{10} N / m ^2\) undergoes elastic strain of \(0.04 \%\). The energy per unit volume stored in the rod in SI unit is:

Two identical cells, when connected either in parallel or in series gives same current in an external resistance \(5\,\Omega\). The internal resistance of each cell will be \(.............\,\Omega\).

A rectangles solid box of length \(0.3\, m\) is held horizontally, with one of its sides on the edge of a platform of height \(5\,m\). When released, it slips off the table in a very short time \(= 0.01\, s\), remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to:

The \(X-Y\) plane be taken as the boundary between two transparent media \(M _{1}\) and \(M _{2} . M _{1}\) in \(Z \geq 0\) has a refractive index of \(\sqrt{2}\) and \(M _{2}\) with \(Z <0\) has a refractive index of \(\sqrt{3}\). A ray of light travelling in \(M_{1}\) along the direction given by the vector \(\overrightarrow{ A }=4 \sqrt{3 i }-3 \sqrt{3 \hat{j}}-5 \hat{ k }\), is incident on the plane of separation. The value of difference between the angle of incident in \(M _{1}\) and the angle of refraction in \(M _{2}\) will be \(....\) degree.

A current of \(1\,A\) is flowing on the sides of an equilateral triangle of side \(4.5\times10^{-2}\,m\) . The magnetic field at the centre of the triangle will be

Two cars \(P\) and \(Q\) start from a point at the same time in a straight line and their positions are represented by \( x_p(t)=at+bt^2 \) and \(x_Q(t)= ft- t^2\). At what time do the cars have the same velocity \(?\) 

The figure shows a square loop \(L\) of side \(5\, cm\) which is connected to a network of resistances. The whole set up is moving towards right with a constant speed of \(1\, cms^{-1}\). At some instant, a part of \(L\) is in a uniform magnetic field of \(1\, T\), perpendicular to the plane of the loop. If the resistance of \(L\) is \(1.7\,\Omega \), the current in the loop at that instant will be close to.....\(\mu A\)

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle \((\theta)\) of thread deflection in the extreme position will be :

Two inclined planes are placed as shown in figure. A block is projected from the Point \(A\) of inclined plane \(A B\) along its surface with a velocity just sufficient to carry it to the top Point \(B\) at a height \(10 m\). After reaching the Point \(B\) the block slides down on inclined plane \(BC\). Time it takes to reach to the point \(C\) from point \(A\) is \(t (\sqrt{2}+1) s\). The value of \(t\) is........(use \(g =10 m / s ^{2}\) )

The magnetic field of a plane electromagnetic wave is given by \(\vec B\, = {B_0}\hat i\,[\cos \,(kz - \omega t)]\, + \,{B_1}\hat j\,\cos \,(kz - \omega t)\) where \({B_0} = 3 \times {10^{-5}}\,T\) and \({B_1} = 2 \times {10^{-6}}\,T\). The rms value of the force experienced by a stationary charge \(Q = 10^{-4} \,C\) at \(z = 0\) is closet to

When current in a coil changes from \(5\,A\) to \(2\,A\) in \(0 .1\,s,\) average voltage of \(50\,V\) is produced. The self- inductance of the coil is.......\(H\)