Physics Test - 1

Force due to electric field will make the charged particle released from rest to move in the straight line (that of electric field). Since the force due to magnetic field is zero, therefore, the charged particle will move in a straight line.

The ability of the eye lens to adjust its focal length is called power of accommodation. This is done by the ciliary muscles by changing the focal length of the eye lens.

Decrease in GPE of B₁ = Increase in Gravitational PE of B₂ + Increase in elastic PE of spring. 

Again applying law of conservation of mechanical energy at the mean position we get  

When the switch is closed at(t = 0s), no current flows, voltage drop across the inductor is the same as the supply voltage of 1.6 V.

Voltage equation for the circuit, we have

Where i is the current drawn from the source , at t = 0s, i = 0, we thus have

Let d be the distance between the moon and the point at force on mass m is zero then

In new situation we have

As the length of magnet is halved , Magnetic moment M’= m(l) = M/2

Resultant magnetic Moment

Let 'x' be the length of the 4^th rod and the centre of the mass of all the rods lies at origin then X_cm = 0

The frequency at which a wire vibrates is given by:

Here, g is the acceleration due to gravity and l is the length of the wire.

Let ’s express the fundamental frequency of the vibration at T₁ ​=30^∘ C as follows,

Let ’s express the fundamental frequency of the vibration at T₂ ​=10^∘ C as follows

Dividing equation (2) by equation (1), we get,

We can express the linear expansion of the wire due to change in temperature as,

Here, αis the linear expansion coefficient and ΔT is the change in temperature.

Using equation (3), we can rewrite the above equation as,

Substituting 1KHz for f_{1 ​} , 1.001KHz for f₂ ​and −20^∘ C for ΔT in the above equation, we get,

Given: C_p - C_v = 4150 Jkg-1K_-1 and C_p /C_v = 1.4 Or C_p = 1.4 C_v .

Therefore,

1.4 C_v - C_v = 4150

Or C_V = 4150/0.4 = 10375 J kg^-1 K^-1

Moment of inertia (I) = mr²

[I] = [ML² ]

Moment of force (C) = rF

[C] = [r][F] = [L][MLT^-2 ] or [C] = [ML² T^-2 ]

Moment of inertia and moment of a force do not have identical dimensions.

The wavelength of line in cased Baimer series is given by where n = 3,4,5 and R = Rydberg constant.

So, for the Balmer series, the transition takes from third orbit to second for first line spectrum, fourth orbit to second for second line spectrum, etc. Hence, the given transition represents the second line of the Balmer series.

The direction of change in velocity (δw) is given by

...(i)

This can be shown graphically as

For small time intervals, i,e„ δt →O, then the angle between v₁ and v₂ is very small i.e., θ ≈ 0°. So. from Eq. (i), we get ∅ = 90⁰

In linear simple harmonic motion, the velocity d particle is given by

…(i)

Where, ω = angular frequency

A = maximum displacement of amplitude

x = displacement from mean position,

The acceleration d a particle in simple harmonic motion, (SHM) is given by

a = ω² x …(iii)

Here, x = A/2

Also, v = a (given)

[from Eqs. (i) and (ii), we get]

⇒

⇒ 2π/T = √3 [∵ω = 2π/T]

⇒ T = (2π/√3)s

When light enters glass from the vacuum, its wavelength decreases. This is because the speed of light is slower in glass than in vacuum, due to the higher refractive index of glass. According to the formula c = λv, where c is the speed of light, λis the wavelength, and v is the frequency, if the speed of light decreases (as it does in glass), then the wavelength must decrease proportionally to maintain a constant frequency.