Physics

A string of mass per unit length $\mu$  is clamped at both ends such that one end of the string is at x = 0 and the other end at x = L. When string vibrates in fundamental mode, amplitude of the midpoint of string is a and tension is string is F. Find the total oscillation energy (in J) stored in the string.

(Use L = 1m, F = 10 N, a =   $\frac{1}{\pi }m)$

In an imaginary electric field, the electric potential energy of an electron at a distance r from the centre of force field is given by U = kr², where k is a positive constant of appropriate dimensions. If the electron is moving in a circular orbit of radius r about the centre, then the orbital time period of the electron is proportional to:

A railway track (made of iron) is laid in winter when the average temperature is $18°C.$  The track consists of sections of 12.0m placed on after the other. How much gap (in cm) should be left between two such sections so that there is no compression during summer when the maximum temperature goes to $48°C?$  Coefficient of linear expansion of iron = 11 * $10^{-6}/°C$ .

A source of light emits monochromatic visible light of wavelength 500 nm. The source emits light of power 100W. The number of photons emitted per sec of the visible light of the given wavelength is: $(\mathrm{h}\mathrm{c}=1240\mathrm{e}\mathrm{V}.\mathrm{n}\mathrm{m})$

In Young's double slit experiment, the wavelength of red light is 7800 Å and that of blue light is 5200 Å. minimum value of n for which n^th bright band due to red light coincides with (n + 1)^th bright band due to blue light, is:

Three rods of equal mass having length L, L and √2L are joined to form a triangular frame as shown in the figure. The system is rotating about an axis passing through the vertex of the triangle and perpendicular to the plane of the triangle with an angular velocity ω. Find the angular momentum of the system.

Calculate the value of output voltage V₀ (in V) if the Si diode and  Ge diode conduct at 0.7V and 0.3V respectively as shown in figure.

An electron moving with a velocity of 2 m/s along +ve x-axis at a point in a magnetic field experiences a force of 2N along -ve y-axis. If the electron moves with of a velocity of 2 m/s along +ve y-axis at the same point, it experiences a force of 2N along +ve x-axis. Find force that the electron would experience if it were moving with a velocity of 2m/s along z-axis.

A plastic circular disc of radius 10cm is placed on a thin oil film of thickness 2mm, spread over a flat horizontal surface. The torque (N-m) required to spin the disc about its central vertical axis with a constant angular velocity 8 rad/sec is (coefficient of viscosity of oil is 1.0 kg/m-s) (take p = 3.14)

A proton and an $\alpha$ -particle both initially at rest are accelerated in a region of electric potential difference V and gravity free space. The proton is projected with gained kinetic energy against a uniform constant electric field and comes to momentary rest after travelling a distance $S_0$ . If the $\alpha$ -particle is also projected with gained kinetic energy against same electric field, it will come to momentary rest after travelling through: