For the following questions answer them individually
A bead $$P$$ sliding on a frictionless semi-circular string ($$ACE$$) and it is at point $$S$$ at $$t = 0$$ and at this instant the horizontal component of its velocity is $$v$$. Another bead $$Q$$ of the same mass as $$P$$ is ejected from point $$A$$ at $$t = 0$$ along the horizontal string $$AB$$, with the speed $$v$$, friction between the beads and the respective strings may be neglected in both cases. Let $$t_{p}$$ and $$t_{Q} be the respective times taken by beads $$P$$ and $$Q$$ to reach the point $$B$$, then the relation between $$t_{p}$$ and $$t_{Q}$$ is
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The current passing through a conducting loop in the form of equilateral triangle of side $$4\sqrt{3}$$ cm is 2A. The magnetic field at its centroid is $$\alpha\times10^{-5}T.$$ The value of $$\alpha$$ is______.
(Given :$$\mu_{o}=4\pi\times 10^{-7} SI$$ units)
The internal energy of a monoatomic gas is 3nRT. One mole of helium is kept in a cylinder having internal cross section area of 17 $$cm^{2}$$ and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises by $$4^{o}C$$, then the piston will move ____ cm.
(atmospheric pressure= $$10^{5}$$ Pa)
A prism of angle $$75^{o}$$ and refractive index $$\sqrt{3}$$ is coated with thin film of refractive index 1.5 only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be______.
($$\sin 15^{o}$$ = 0.25 and $$\sin 25^{o}$$ = 0.43)
Two charges $$7\mu C \text{ and } -2\muC$$ are placed at (-9,0,0)cm and (9,0,0)cm respectively in an external field $$E=\frac{A}{r^{2}}\overline{r}$$, where $$A=9\times 10^{5}N/C.m^{2}.$$ Considering the potential at infinity is 0, the electrostatic energy of the configuration is ______J.
Which of the following pair of nuclei are isobars of the element?
A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with $$3m/s^{2}$$. At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is 5 m/s. The initial height of the airplane is ___ m.
($$g = 10 m/s^{2}$$)
When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The angle of refracted
beam with respect to the normal is ______ .
($$\tan^{-1}$$ (1.52) = $$57.7^{o}$$, refractive indices of air and glass are 1.00 and 1.52, respectively.)
An air bubble of volume 2.9 $$cm^{3}$$ rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is $$17^{o}$$C. The volume of the bubble when it reaches the surface, where the water temperature is $$27^{o}$$C, is ______$$cm^{3}$$.
($$g = 10 m/s^{2}$$, density of water = $$10^{3} kg/m^{3}$$, and 1 atm pressure is $$10^{5}$$ Pa)
A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s.
The EMF induced in the loop is ____ mV.
