Physics

A wire of length 30cm, stretched between rigid supports, has it's n^th and (n + 1)^th harmonics at 400Hz and 450Hz, respectively, If tension in the string is 2700N, it's linear mass density is ____________kg/m.

A parallel plate capacitor with width 4cm, length 8cm and separation between the plates of 4mm is connected to a battery of 20V. A dielectric slab of dielectric constant 5 having length 1cm, width 4cm and thickness 4mm is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be ___________ ${\in }_{0}J.$  

(Where ${\in }_0$  is the permittivity of free space)

A modulating signal 2sin (6.28 * 10⁶)t is added to the carrier signal 4 sin(12.56 *10⁹)t for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passes through a band pass filter. The bandwidth of the output signal of band pass filter will be_________ MHz.

As shown in the figure, in steady state, the charge stored in the capacitor is ____________* 10^-6C.

A conducting circular loop is placed in X – Y plane in presence of magnetic field $\overrightarrow{B}=\left(3t^3\widehat{j}+3t^2\widehat{k}\right)$  in SI unit. If the radius of the loop is 1m. The induced emf in the loop, at time, t = 2s is npV. The value of n is__________.

A thin prism of angle 6° and refractive index for yellow light (n_Y) 1.5 is combined with another prism of angle 5° and n_Y = 1.55. The combination produces no dispersion. The net average deviation $\left(\delta \right)$  produced by the combination is   ${\left(\frac{1}{x}\right)}^o$ . The value of x is____________.

The velocity of a small ball of mass 0.3g and density 8 g/cc when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3 g/cc, then the value of viscous force acting on the ball will be x * 10^-4 N, value of x is________. [use g = 10 m/s²]

In the given figure of meter bridge experiment, the balancing length AC corresponding to null deflection of the galvanometer is 40 cm. The balancing length, if the radius of the wire AB is doubled, will be__________cm.

In an experiment to determine the Young's modulus, steel wires of five different lengths (1, 2, 3, 4, and 5m ) but of same cross section (2 mm²) were taken and curves between extension and load were obtained. The slope (extension / load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is x * 10¹¹ Nm^-2, then the value of x is________.

A metal wire of length 0.5 m and cross-sectional area 10^-4 m² has breaking stress 5 * 10⁸ Nm^-2. A block of 10 kg is attached at one of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be ________ ms^-1.