Two circular discs of radius each 10 cm are joined at their centres by a rod of length 30 cm and mass 600 gm as shown in figure.
If the mass of each disc is 600 gm and applied torque between two discs is \(43 \times 10^{5}\) dyne cm, the angular acceleration of the discs about the given axis \(AB\) is ___________\(rad/s^{2}\).

A particle of mass \({m}\) is suspended from a ceiling through a string of length \(L\). The particle moves in a horizontal circle of radius \(r\) such that \({r}=\frac{{L}}{\sqrt{2}}\). The speed of particle will be:

A small metallic sphere of diameter 2 mm and density \(10.5 g / cm ^3\) is dropped in glycerine having viscosity 10 Poise and density \(1.5 g / cm ^3\) respectively. The terminal velocity attained by the sphere is ___________ \(cm / s\).
\(\left(\pi=\frac{22}{7}\right.\) and \(\left.g=10 m / s ^2\right)\)

Two Carnot engines \(A\) and \(B\) are operated in series. The first one, \(A,\) receives heat at \(T_1(= 600\,K)\) and rejects to a reservoir at temperature \(T_2.\) The second engine \(B\) receives heat rejected by the first engine and, in turns, rejects to a heat reservoir at \(T_3 (=400\,K).\) Calculate the temperature \(T_2\) if the work outputs of the two engines are equal   ..... \(K\)

A wire of length \(2\,L\) is made by joining two wires \(A\) and \(B\) of same lengths but different radii \(r\) and \(2r\) and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire \(A\) is \(p\) and that in \(B\) is \(q\) then the ratio \(p : q\) is

A particle of mass \(20\,g\) is released with an initial velocity \(5\,m/s\) along the curve from the point \(A,\) as shown in the figure. The point \(A\) is at height \(h\) from point \(B.\) The particle slides along the frictionless surface. When the particle reaches point \(B,\) its angular momentum about \(O\) will be ......... \(kg - m^2/s\). [Take \(g = 10\,m/s^2\) ]

A raindrop with radius \(R=0.2\, {mm}\) fells from a cloud at a height \(h=2000\, {m}\) above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attainde by the raindrop is : (In \({ms}^{-1}\)) [Density of water \(f_{{w}}=1000\;{kg} {m}^{-3}\) and density of air \(f_{{a}}=1.2\; {kg} {m}^{-3}, {g}=10 \;{m} / {s}^{2}\) Coefficient of viscosity of air \(=18 \times 10^{-5} \;{Nsm}^{-2}\) ]

An \(\alpha\)-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their De-Broglie wavelength:

A laser beam has intensity of \( 4.0\times10^{14} W/m^{2} \). The amplitude of magnetic field associated with beam is__________ T. (Take \( \epsilon_{0}=8.85\times10^{-12} C^{2}/Nm^{2} \) and \( c=3\times10^{8} m/s \))

A capacitor \(C\) is fully charged with voltage \(V _{0}\) After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance \(\frac{ C }{2} .\) The energy loss in the process after the charge is distributed between the two capacitors is\(.........\)\(CV _{0}^{2}\)

Electron beam used in an electron microscope, when accelerated by a voltage of \(20\,kV\). has a de-Broglie wavelength of \(\lambda_0\). If the voltage is increased to \(40\,kV\). then the de-Broglie wavelength associated with the electron beam would be:

On celcius scale the temperature of body increases by \(40^{\circ} \mathrm{C}\). The increase in temperature on Fahrenheit scale is _______.