A block of metal weighing \(2 \,kg\) is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of \(1 \,kgs ^{-1}\) and at a speed of \(10 \,ms ^{-1}\). Then, the initial acceleration of the block, in \(ms ^{-2}\), will be .................

The time taken by a block of mass \(m\) to slide down from the highest point to the lowest point on a rough inclined plane is \(50\%\) more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at \(45^\circ\) with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is _____.

The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is ___________ cm.

Given below are two statements: \(Statement\) \((I)\) : The limiting force of static friction depends on the area of contact and independent of materials. \(Statement\) \((II)\) : The limiting force of kinetic friction is independent of the area of contact and depends on materials. In the light of the above statements, choose the most appropriate answer from the options given below:

A series \(L C R\) circuit has \(L=0.01\,H, R=10\,\Omega\) and \(C =1\,\mu F\) and it is connected to ac voltage of amplitude \(\left( V _{ m }\right) 50\,V\). At frequency \(60 \%\) lower than resonant frequency, the amplitude of current will be approximately \(...............\,mA\)

Match List\(-I\) with List\(-II\) :

List\(-I\)	List\(-II\)
\((a)\) \(\omega L\,>\,\frac{1}{\omega C}\)	\((i)\) Current is in phase with \(emf\)
\((b)\) \(\omega {L}=\frac{1}{\omega {C}}\)	\((ii)\) Current lags behind the applied \(emf\)
\((c)\) \(\omega {L}\, < \,\frac{1}{\omega {C}}\)	\((iii)\) Maximum current occurs
\((d)\) resonant frequency	\((iv)\) Current leads the \(emf\)

Choose the correct answer from the options given below :

Consider a badminton racket with length scales as shown in the figure.If the mass of the linear and circular portions of the badminton racket are same \((M)\) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, \(\frac{r}{2}\) distance from the end \(A\) of the handle will be ....... \(Mr^2\)?

When the temperature of a metal wire is increased from \(0^{\circ} \,C\) to \(10^{\circ}\, C\), its length increases by \(0.02 \% .\) The percentage change in its mass density will be closest to:

A cube has side length \(5\) cm and modulus of rigidity \(10^5\) N/m\(^2\). The displacement produced by a force of \(10\) N in the upper face of cube is _____ mm.

An electric field \(\vec E\, = (25 \hat i + 30 \hat j)\,NC^{-1}\) exists in a region of space. If the potential at the origin is taken to be zero then the potential at \(x\, = 2\, m, y\, = 2\, m\) is......\(volt\)

A circular coil of radius \(10\, cm\) is placed in a uniform magnetic field of \(3.0 \times 10^{-5}\, T\) with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in \(0.2\,s.\) The maximum value of \(EMF\) induced (in \(\mu V\) ) in the coil will be close to the integer\(....\mu V\)

A monochromatic light of wavelength \(6000\)A is incident on the single slit of width \(0.01 \mathrm{~mm}\). If the diffraction pattern is formed at the focus of the convex lens of focal length \(20 \mathrm{~cm}\), the linear width of the central maximum is _______.

In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to: \(A\). pure inductor. \(B\). pure capacitor. \(C\). pure resistor. \(D\). combination of an inductor and capacitor. Choose the correct answer from the options given below: