A plane electromagnetic wave of frequency 500 MHz is travelling in vacuum along y-direction. At a particular point in space and time, $\vec B = 8.0 \times 10^{-8} \hat z T$. The value of electric field at this point is:
(speed of light = $3 \times 10^8 ms^{-1} $)
$\hat x , \hat y , \hat z $ are unit vectors along x, y and z directions.
(A) $24 \hat x V/m $
(B) $2.6 \hat x V/m $
(C) $-24 \hat x V/m $
(D) $-2.6 \hat y V/m $ Continue reading A plane electromagnetic wave of frequency 500 MHz ….
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 _ _ _ _ . Continue reading A fringe width of 6 mm was produced ….
For an electromagnetic wave traveling in free space, the relation between average energy densities due to electric $(U_e)$ and magnetic $(U_m)$ fields is:
(A) $U_e > U_m $
(B) $U_e = U_m $
(C) $U_e \neq U_m $
(D) $U_e < U_m $ Continue reading For an electromagnetic wave traveling in free space ….
The maximum and minimum distances of a comet from the Sun are $1.6 \times 10^{12}$ m and $8.0 \times 10^{10} $ m respectively. If the speed of the comet at the nearest point is $6 \times 10^4 $ m/s, the speed at the farthest point is:
(A) $3.0 \times 10^3 $ m/s
(B) $1.5 \times 10^3 $ m/s
(C) $4.5 \times 10^3 $ m/s
(D) $6.0 \times 10^3 $ m/s Continue reading The maximum and minimum distances of a comet ….
A sinusoidal voltage of peak value 250 V is applied to a series LCR circuit, in which $R=8 \Omega$, $L=24 mH$ and $C=60 \mu F $. The value of power dissipated at resonant condition is ‘x’ kW. The value of x to the nearest integer is _ _ _ _ . Continue reading A sinusoidal voltage of peak value 250 V ….
Since cos x lies between -1 & 1, the left hand side lies between 4 & 16.
Since sin x lies between -1 & 1 or $sin^8 x $ lies between 0 & 1, the right hand side lies between 2 & 4.
The two sides can become equal only when each one of them is equal to 4.
This happens when cos x of the left hand side is equal to -1 and sin x of the right hand side is equal to 0.
This can only happen when x is an odd multiple of $\pi $.
So, $x=(2n+1)\pi $ where n is any integer.
Let a vector $\alpha \hat i + \beta \hat j $ be obtained by rotating the vector $\sqrt 3 \hat i + \hat j $ by an angle $45^\circ $ about the origin in counterclockwise direction in the first quadrant. Then the area of triangle having vertices $(\alpha , \beta )$, $(0, \beta )$ and (0, 0) is equal to:
(A) $2\sqrt 2 $
(B) $\frac {1}{2}$
(C) 1
(D) $\frac {1}{\sqrt 2 }$ Continue reading Let a vector $\alpha \hat i + \beta \hat j $ be obtained by ….
