A particle of mass \(250\,g\) executes a simple harmonic motion under a periodic force \(F =(-25\,x) N\). The particle attains a maximum speed of \(4\,m / s\) during its oscillation. The amplitude of the motion is \(...........cm\).

In the reported figure, heat energy absorbed by a system in going through a cyclic process is \(......\,\pi J\)

A fringe width of \(\,6 mm\) was produced for two slits separated by \(1\, mm\) apart. The screen is placed \(10\, m\) away. The wavelength of light used is \('x'\, nm.\) The value of \('x'\) to the nearest integer is

For the photoelectric effect, the maximum kinetic energy \(\left(E_{\mathrm{k}}\right)\) of the photoelectrons is plotted against the frequency \((v)\) of the incident photons as shown in figure. The slope of the graph gives _______.

The number of electrons flowing per second in the filament of a \(110 \mathrm{~W}\) bulb operating at \(220 \mathrm{~V}\) is _______. (Given \(\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\) )

In Young's double slit arrangement, slits are separated by a gap of \(0.5\, mm ,\) and the screen is placed at a distance of \(0.5\, m\) from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light of \(5890\, A^o\) is

One end of a straight uniform \(1\; \mathrm{m}\) long bar is pivoted on horizontal table. It is released from rest when it makes an angle \(30^{\circ}\) from the horizontal (see figure). Its angular speed when it hits the table is given as \(\sqrt{\mathrm{n}}\; \mathrm{s}^{-1},\) where \(\mathrm{n}\) is an integer. The value of \(n\) is

A sphere of capacitance \(100\) pF is charged to a potential of \(100\) V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is \(\alpha \times 10^{-7}\) J. The value of \(\alpha\) is __________. (combined capacitance of spheres is \(200\) pF)

In a meter bridge experiment \(\mathrm{S}\) is a standard resistance. \(\mathrm{R}\) is a resistance wire. It is found that balancing length is \(l=25 \;\mathrm{cm} .\) If \(\mathrm{R}\) is replaced by a wire of half length and half diameter that of \(\mathrm{R}\) of same material, then the balancing distance \(\left.l^{\prime} \text { (in } \mathrm{cm}\right)\) will now be

A projectile is projected with velocity of \(25\, m / s\) at an angle \(\theta\) with the horizontal. After t seconds its inclination with horizontal becomes zero. If \(R\) represents horizontal range of the projectile, the value of \(\theta\) will be : [use \(g =10 m / s ^{2}\) ]

A parallel plate capacitor with plates of area \(1\,m^2\) each, are at a separation of \(0.1\,m.\) If the electric field between the plates is \(100\,N/C,\) the magnitude of charge on each plate

A thin prism \(\mathrm{P}_1\) with angle \(4^{\circ}\) made of glass having refractive index 1.54 , is combined with another thin prism \(\mathrm{P}_2\) made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism \(P_2\) in degrees is _______.