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 elastic limit of brass is \(379\,MPa.\) .......... \(mm\) should be the minimum diameter of a brass rod if it is to support a \(400\,N\) load without exceeding its elastic limit .

A series \(LR\) circuit is connected to an ac source of frequency \(\omega \) and the inductive reactance is equal to \(2R\). A capacitance of capacitive reactance equal to \(R\) is added in series with \(L\) and \(R\). The ratio of the new power factor to the old one is

There are \(100\) divisions on the circular scale of a screw gauge of pitch \(1 \mathrm{~mm}\). With no measuring quantity in between the jaws, the zero of the circular scale lies \(5\) divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found the \(4\) linear scale divisions are clearly visible while \(60\) divisions on circular scale coincide with the reference line. The diameter of the wire is _______.

If \(\overrightarrow{ P }=3 \hat{ i }+\sqrt{3} \hat{ j }+2 \hat{ k }\) and \(\overrightarrow{ Q }=4 \hat{ i }+\sqrt{3} \hat{ j }+2.5 \hat{ k }\) then, The unit vector in the direction of \(\overrightarrow{ P } \times \overrightarrow{ Q }\) is \(\frac{1}{x}(\sqrt{3} \hat{i}+\hat{j}-2 \sqrt{3} \hat{k})\). The value of \(x\) is

The equivalent resistance between \(A\) and \(B\) as shown in figure is \(........\,k\Omega\)

The helium and argon are put in the flask at the same room temperature ( 300 K). The ratio of average kinetic energies (per molecule) of helium and argon is :
(Give : Molar mass of helium \(=4 \mathrm{~g} / \mathrm{mol}\), Molar mass of argon \(=40 \mathrm{~g} / \mathrm{mol}\))

If the deBroglie wavelength of an electron is equal to \(10^{-3}\) times the wavelength of a photon of frequency \(6\,\times 10^{14}\,Hz,\) then the speed of electron is equal to: (Speed of light \(=3\times 10^8\,m/s\,;\) Planck’s constant \(=6.63\times 10^{-34}\,J.s\,;\) Mass of electron \(=9.1\times 10^{-31}\,kg\) )

The figure shows three circuits \(I, II\) and \(III\) which are connected to a \(3\,V\) battery. If the powers dissipated by the configurations \(I, II\) and \(III\) are \(P_1 , P_2\) and \(P_3\) respectively, then

Four particles \(A, B, C\) and \(D\) with masses \(m_A=m, m_B=2m, m_C=3m\) and \(m_D=4m\) are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is

A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is \(y \pi \times 10^{-2} \mathrm{~s}\), where the value of \(y\) is ________.
(Acceleration due to gravity, \(g=10 \mathrm{~m} / \mathrm{s}^2\), density of water \(=10^3 \mathrm{~kg} / \mathrm{m}^3\) )

A block of \(\sqrt{3}\,kg\) is attached to a string whose other end is attached to the wall. An unknown force \(F\) is applied so that the string makes an angle of \(30^{\circ}\) with the wall. The tension \(T\) is \(...........\,N\) :(Given \(g =10\,ms ^{-2}\) )

In the given circuit, the breakdown voltage of the Zener diode is \(3.0 \mathrm{~V}\). What is the value of \(\mathrm{I}_z\) ?