A ball of mass \(4\, kg\), moving with a velocity of \(10\, ms ^{-1}\), collides with a spring of length \(8\, m\) and force constant \(100\, Nm ^{-1}\). The length of the compressed spring is \(x\, m\). The value of \(x\), to the nearest integer, is ........ .

When a diode is forward biased, it has a voltage drop of \(0.5\, V.\) The safe limit of current through the diode is \(10\, mA\). If a battery of emf \(1.5\, V\) is used in the circuit, the value of minimum resistance to be connected in series with the diode so that the current does not exceed the safe limit is\(.....\Omega\)

The velocity of a small ball of mass ' \(m\) ' and density \(d _{1}\), when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is \(d _{2}\), then the viscous force acting on the ball, will be

A uniform chain of length \(3\, meter\) and mass \(3\, {kg}\) overhangs a smooth table with \(2\, meter\) laying on the table. If \(k\) is the kinetic energy of the chain in joule as it completely slips off the table, then the value of \({k}\) is (Take \(\left.g=10\, {m} / {s}^{2}\right)\)

A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm . If D and d are the total distance and displacement covered by the particle in 12.5 s , then \(\frac{\mathrm{D}}{\mathrm{d}}\) is ________.

Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is \(M,\) radius of its top, \(R\) and height, \(H\), then its moment of inertia about its axis is

Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance \(2000 \,\Omega\) is used to measure the potential difference across \(500 \,\Omega\) resister, the reading of the voltmeter will be ............... \(V\)

Light emerges out of a convex lens when a source of light kept at its focus. The shape of wavefront of the light is _______.

A capacitor of capacitance \(50 \; pF\) is charged by \(100 \; V\) source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is \(\dots \; nJ\).

The distance between two consecutive points with phase difference of \(60^{\circ}\) in a wave of frequency \(500\,Hz\) is \(6.0\,m\). The velocity with which wave is traveling is \(.........km / s\)

An object is dropped from a height \(h\) from the ground. Every time it hits the ground it looses \(50\%\) of its kinetic energy. The total distance covered as \(t \to \infty \) is

The period of oscillation of a simple pendulum is \(T =2 \pi \sqrt{\frac{ L }{ g }} .\) Measured value of \( L \) is \(1.0\, m\) from meter scale having a minimum division of \(1 \,mm\) and time of one complete oscillation is \(1.95\, s\) measured from stopwatch of \(0.01 \,s\) resolution. The percentage error in the determination of \(g\) will be ..... \(\%.\)