MHT CET 2019 :: Physics :: General questions

• Physics - General questions

The figure shows the circular coil carrying current l kept very close but not touching at a point  A on a straight conductor carrying the same current l. The magnitude of magnetic induction  at the centre of the circular coil will be 

Answer:

Explanation:

 Magnetic  induction at the centre of circular current carrying loop.

$B_{1}=\frac{\mu_{0}i}{2r}$              (downward direction )

 Magnetic induction at the centre O due to straight  wire,

$B_{2}=\frac{\mu_{0}}{2\pi}\frac{i}{r}$   (upward direction)

 Net magnetic induction at O,

 $B=B_{1}-B_{2}=\frac{\mu_{0}i}{2r}-\frac{\mu_{0}}{2\pi}.\frac{i}{r}$

 $=\frac{\mu_{0}i}{2r}\left[1-\frac{1}{\pi}\right]$  [ downward direction]

 Hence, there are no option correct.

The fundamental frequency of the sonometer wire increases by 9 Hz if its tension is increased by 69%, keeping the length constant.The frequency  of the wire is 

Answer:

Explanation:

We know that freequency of vibration of a strtched string is given by 

$v=\frac{1}{2l}\sqrt{\frac{T}{m}}$

 where, T= tension in string

m= mass /length

 and l= length of string 

New freequency,

  $v'=v+9=\frac{1}{2l}\sqrt{\frac{T+(69/100)T}{m}}$

 $\Rightarrow $  $\frac{v}{v'}=\sqrt{\frac{T}{\frac{169}{100}T}}\Rightarrow \frac{v}{v+9}=\sqrt{\frac{100}{169}}=\frac{10}{13}$

 $\Rightarrow 13 v=10v+90$

 v=30 Hz

The refractive index of the material of crystal is 1.68 and that of castor oil is 1.2. When  a ray of  light passes from oil  to glass, its velocity will change by a factor 

Answer:

Explanation:

 We know , refractive index of crystal w.r.t oil,

 $\mu_{co}=\frac{\mu_{c}}{\mu_{o}}$= speed of light in oil/ speed of light in crystal

 where, $\mu_{c}$=  absolute  refractive index of crystal  w.r.t vacuum

    and $\mu_{o}$ = absolute  refractive index of oil w.r.t  vacuum.

 $\mu_{co}=\frac{1.68}{1.2}=\frac{7}{5}$  = speed in oli/ speed in crystal

 Fractional change in velocity ,

 when light travel from oil  to  crystal =  speed in crystal/ speed in oil= $\frac{5}{7}$

In a hydrogen atom, an electron of charge e revolves in an orbit of radius r with speed v. Then, the magnetic moment associated with the electron is 

Answer:

Explanation:

Magnetic moment of  revolving electron,

   $\mu_{e}=i \times A$

 where, i= current and A= area

 $\therefore$ $\mu_{e}=\frac{e}{T} \times \pi r^{2}$      (As current, i= $\frac{charge}{time}=\frac{e}{T}$)

 where, T= time period of revolution and r= radius of orbit

$\mu_{e}=\frac{e}{2\pi r} \times v \times \pi r^{2}$

 ( $\because$   Time period (T)= $\frac{ distance }{ speed}$)

 where, v= velocity of revolving electron

$\Rightarrow$    $\mu_{e}=\frac{evr}{2} $

 Hence, the magnetic moment of revolving electron is $\frac{evr}{2}$

In amplitude  modulation, the amplitude of carrier wave is  A_c and that of the modulating signal is A_m . In practice, the ratio of A_m to A_c is kept less than or equal to one , to avoid

Answer:

Explanation:

Modulation index,  $\mu_{}=\frac{A_{m}}{A_{c}} \leq1$ is carried by the carrier wave, i.e, there is no signal distortion

• Physics - General questions