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Which instrument is used for measuring the relative humidity of the atmosphere?
Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and current I, would be
Resistance,R=PotentialdifferenceCurrent=Vi=WQi (∵Potential difference is equal to work done per unit charge)
So, dimensions of R
=[Dimensionsofwork][Dimensionsofcharge][Dimensionsofcurrent]
=ML2T−2[IT][I]=ML2T−3I−2
An inclined plane making an angle β with horizontal. A projectile projected from the bottom of the plane with a speed u at angle αα with horizontal, then its maximum range Rmax is
The expression of horizontal Range R =2u2sin(α−β)cosαgcos2β
From identity
2 sin A cos B = sin (A+B) + sin (A−B)
2 sin (α−β) cos α = sin (2α−β) + sin (−β)
R =u2gcos2β[sin(2α−β)−sinβ]
Range R along incline is maximum if 2α−β=π/2 (as β is fixed)
The acceleration of an electron in the first orbit of the hydrogen atom (n=1) is :
For H−atom (n=1)
mv2r=14πϵoe2r2−(1)
mvr=h2π−(2)
Squaring (2)
m2v2r2=h24π2
Dividing both sides by r3,
m2v2r=h24πr3⇒v2r=h24π2r3m2
∴accelration=h24π2r3m2
A laser light of wavelength 660 nm is used to weld Retina detachment. If a laser pulse of width 60 ms and power 0.5 kW is used, the approximate number of photons in the pulse are (Take Planck's Constant, h=6.62×10−34 J s
Power P is given as ,
A signal of frequency 20 kHz and peak voltage of 5 Volt is used to modulate a carrier wave of frequency 1.2 MHz and peak voltage 25 Volts. Choose the correct statement.
Modulation idex =m=VmVc=525
=15=0.2
carrier Frequency 1.2×103kHz
fc = 1200 kHz
lower side band frequency f1 = 1200 - 20 = 1180 KHz
Upper band frequency f2 = 1200 + 20 = 1220 KHz
Charges Q, 2Q and −Q are given to three concentric conducting spherical shells A, B and C respectively, as shown in the figure. The ratio of charges on the inner and outer surfaces of the shell C will be
Due to induction of charge on surface facing each other will be equal and opposite.
Ratio =-32
A stationary source (see figure) emits sound waves of frequency f towards a stationary wall. If an observer moving with speed uu in a direction perpendicular to the wall measures a frequency f′=11/8f at the instant shown, then uu is related to the speed of sound Vs as
This is the case of Doppler's effect in reflected sound.
The apparent frequency is given by
f′=fv+v0v−vs
Given,f′=118f
v0= u
vs=0 (stationary source)
v=Vs
∴118f=vs+ucos60Vs
118=1+u2Vs
38=u2Vs
Vs=43u
A coil, in the shape of an equilateral triangle of side l, is suspended between two pole pieces of a permanent magnet, such that the magnetic field B is in the plane of the coil. If due to current I in the triangle, a torque τ acts on it, the side l of the triangle is
Torque acting on an equilateral triangle in a magnetic field B is
τ=IAB sinθ
Area ofΔLMN:A=34l2
and θ=90o
Substituting the given values in the expression for torque, we have
τ=I×34l2 Bsin90°=34I l2B
∴l=2τ3BI12
Consider a collection of a large number of particles each moving with speed v. The direction of velocity is randomly distributed in the collection. Find the magnitude of the relative velocity between a pair of particles averaged over all the pairs in the collection.
Consider any two particles whose velocity vector particles making angle θ.
Relative velocity vAB = vA - vB
⇒vrel=v2+v2-2v2cosθ
⇒vrel=2vsinθ2
Average of vrelπππ∫02πverldθ∫02πdθ=4vπ
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