A spherical body of mass \(2\,kg\) starting from rest acquires a kinetic energy of \(10000\,J\) at the end of \(5^{\text {th }}\) second. The force acted on the body is \(.....N\)

A light ray enters a solid glass sphere of refractive index \(\mu=\sqrt{3}\) at an angle of incidence \(60^{\circ}\). The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is......

A cyclotron is used to accelerate protons. If the operating magnetic field is \(1.0\,T\) and the radius of the cyclotron 'dees' is \(60 cm\), the kinetic energy of the accelerated protons in \(MeV\) will be. [use \(m _{p}=1.6 \times 10^{-27} kg , e =1.6 \times 10^{-19} C\) ]

Two \(10 \; cm\) long, straight wires, each carrying a current of \(5 \; A\) are kept parallel to each other. If each wire experienced a force of \(10^{-5} \; N\), then separation between the wires is \(\dots \; cm\).

Find the correct combination of A, B, C and D inputs which can cause the LED to glow

In the given figure, an inductor and a resistor are connected in series with a battery of emf \(E\) volt. \(\frac{E^a}{2 b }\,J / s\) represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of \(\frac{ b }{ a }\) will be ............

A telescope has an objective lens of focal length \(150\,\,cm\) and an eyepiece of focal length \(5 \,\,cm.\) If a \(50\,\,m\) tall tower at a distance of \(1\,\,km\) is observed through this telescope in normal setting, the angle formed by the image of the tower is \(\theta \), then \(\theta \) is close to.....\(^o\)

Steel ruptures when a shear of \(3 .5 \times 10^8\,\,N\,m^{-2}\) is applied. The force needed to punch a \(1\,cm\) diameter hole in a steel sheet \(0.3\,cm\) thick is nearly

A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of \(10\,cm\). The separation between the two lenses is \(2\,cm\). The focal lengths of the component lenses

A massless spring \((k = 800\, N/m)\), attached with a mass \((500\, g)\) is completely immersed in \(1\, kg\) of water. The spring is stretched by \(2\, cm\) and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and specific heat of mass \(= 400\, J/kg\, K\), specific heat of water \(= 4184\, J/kg\, K\))

A body of mass \(m\) is suspended by two strings making angles \(\theta_1\) and \(\theta_2\) with the horizontal ceiling with tensions \(T_1\) and \(T_2\) simultaneously. \(T_1\) and \(T_2\) are related by \(T_1=\sqrt{3} T_2\). the angles \(\theta_1\) and \(\theta_2\) are

Two plane polarized light waves combine at a certain point whose electric field components are :
\(\begin{aligned} & \mathrm{E}_1=\mathrm{E}_0 \sin \omega \mathrm{t} \\ & \mathrm{E}_2=\mathrm{E}_0 \sin \left(\omega \mathrm{t}+\frac{\pi}{3}\right)\end{aligned}\)
Find the amplitude of the resultant wave.