The rain drop of mass \(1\) g, starts with zero velocity from a height of \(1\) km. It hits the ground with a speed of \(5\) m/s. The work done by the unknown resistive force is _______ J. (take \(g = 10\) m/s\(^2\))

A certain charge \(Q\) is divided into two parts \(q\) and \((Q-q) .\) How should the charges \(Q\) and \(q\) be divided so that \(q\) and \((Q-q)\) placed at a certain distance apart experience maximum electrostatic repulsion?

A travelling harmonic wave is represented by the equation \(y(x, t) = 10^{-3}\,sin\,(50t + 2x)\), where \(x\) and \(y\) are in meter and \(t\) is in seconds. Which of the following is a correct statement about the wave?

If the Earth has no rotational motion, the weight of a person on the equator is \(W\). Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weight \(\frac{3}{4}\,W\) . Radius of the Earth is \(6400\, km\) and \(g = 10\, m/s^2\)

Two blocks of masses \(2\) kg and \(1\) kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held at rest at the same horizontal level and then released. The distance traversed by the centre of mass in \(2\) s is _______ m. (Take \(g = 10\) m/s\(^2\))

In a Young's double slit experiment, the intensities at two points, for the path difference \(\frac{\lambda}{4}\) and \(\frac{\lambda}{3}\) ( \(\lambda\) being the wavelength of light used) are \(I_1\) and \(I_2\) respectively. If \(I_0\) denotes the intensity produced by each one of the individual slits, then \(\frac{ I _1+ I _2}{ I _0}=..............\)

A body of mass \(4 \mathrm{~kg}\) experiences two forces \(\overrightarrow{\mathrm{F}}_1=5 \hat{\mathrm{i}}+8 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{F}}_2=3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}\). The acceleration acting on the body is _______.

A proton of mass ' \(m_{\mathrm{p}}\) ' has same energy as that of a photon of wavelength ' \(\lambda\) '. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is _______.

Which of the following is not a dimensionless quantity?

For designing a voltmeter of range \(50\,V\) and an ammeter of range \(10\,mA\) using a galvanometer which has a coil of resistance \(54\,\Omega\) showing a full scale deflection for \(1\,mA\) as in figure. \((A)\) for voltmeter \(R \approx 50\,k\Omega\) \((B)\) for ammeter \(r \approx 0.2\,\Omega\) \((C)\) for ammeter \(r \approx 6\,\Omega\) \((D)\) for voltmeter \(R \approx 5\,k \Omega\) \((E)\) for voltmeter \(R \approx 500 \Omega\) Choose the correct answer from the options given below

A hoop of radius \(r\) and mass \(m\) rotating with an angular velocity \(\omega_0\) is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

An ideal gas undergoes a process maintaining relation between pressure \((P)\) and volume \((V)\) as \(P = P_o\left(1 + \left(\dfrac{V_o}{V}\right)^2\right)^{-1}\), where \(P_o\) and \(V_o\) are constants. If two samples \(A\) and \(B\) (two moles each) with initial volumes \(V_o\) and \(3V_o\) respectively undergo above mentioned process and attain same pressure, then the difference at the temperatures of these samples, \(T_B - T_A\) is _____. (\(R = \) gas constant)

A \(0.5 \,kg\) block moving at a speed of \(12 \,ms ^{-1}\) compresses a spring through a distance \(30\, cm\) when its speed is halved. The spring constant of the spring will be \(Nm ^{-1}\).