Home / Free Subjects / physics

A DC motor works by a force exerted on a current-carrying coil in a magnetic field. To ensure the motor continues to rotate in one direction, the direction of the current in the coil must be reversed every half rotation. The commutator is a device that performs this function, reversing the current and ensuring that the torque always acts in the same direction, leading to continuous rotation.

1. Identify the velocity equation: v=10+2t2

2. Recall relationship between velocity and acceleration: Acceleration (a) is the first derivative of velocity with respect to time ( $a=\frac{dv}{dt}$ )

3. Differentiate the velocity equation:

1. $a=\frac{d}{dt}(10+2t^2)$
2. a=0+2×2t
3. a=4t

4. Substitute the given time (t=5 s):

1. $a=4×5=20 ms^{-1}$
2. $\therefore a=20ms^{-1}$

"The frictional force is independent of the area of the surfaces in contact." is True.

1. Sliding friction does not depend on the contact area under normal conditions.
2. Even if one surface is larger, the frictional force remains the same.

"The frictional force depends on the nature of the surfaces in contact." is True

1. Friction is affected by how rough or smooth the surfaces are.
2. Example: Rubber on concrete vs. metal on ice.

"The frictional force depends on the speed of sliding." is False

1. Under most everyday conditions, sliding friction remains constant regardless of speed.
2. Speed only affects friction in special cases (e.g., very high speeds or fluid-lubricated surfaces).

"The frictional force is directly proportional to the normal reaction." is True

1. This is based on the standard friction equation:
2. Friction = μ × Normal Force

The Correct Combination:

1. Statements I, II, and IV are true
2. Correct Option: A. I, II and IV

The electric potential difference (or voltage) between two points is defined as the work done per unit positive charge in moving the charge from one point to the other. It is measured in Volts (V), which is equivalent to Joules per Coulomb (J/C)

1. The deviation (δ) of a plane mirror is the angle between the incident ray's original path and the reflected ray's path. The formula δ=180∘−2i, where i is the angle of incidence (measured from the normal).

2. Identify given deviation: δ=120∘

3. Substitute into the formula and solve for i:

1. 120∘=180∘−2i
2. 2i=180∘−120∘
3. 2i=60∘
4. i=30∘

The relationship between wave velocity (V), frequency (f), and wavelength ($\lambda$ ) is given by the formula $V = f\lambda$ . To find the wavelength, we rearrange the formula to $\lambda = V/f$ . Substituting the given values, $\lambda = 340 m/s / 200 Hz = 1.7$ m.

Total Internal Reflection (TIR) is a phenomenon where a light ray is completely reflected back into the first medium. This occurs only under two specific conditions:

1. The light must travel from an optically denser medium (higher refractive index) to an optically rarer medium (lower refractive index).
2. The angle of incidence must be greater than the critical angle for that specific interface.

Myopia is a sight defect where the person can see near objects clearly but cannot focus on distant objects. The far point for a myopic person is closer than infinity. To correct this, a diverging (concave) lens is needed to form a virtual image of a distant object (at infinity) at the person's far point (2.0 m). Using the lens formula, $1/f = 1/u + 1/v$ , with $u = \infty$ and $v = -2.0$ m (virtual image at far point), we get $1/f = 1/\infty + 1/(-2.0) = 0 - 1/2 = -0.5$ . The focal length is $f = -2.0$ m. The power of the lens (P) is the reciprocal of the focal length in meters: $P = 1/f = 1/(-2.0) = -0.5$ D.

Most liquids expand when heated and contract when cooled. However, water behaves anomalously between 0°C and 4°C. When heated from 0°C to 4°C, water contracts and its density increases, reaching its maximum density at 4°C. When heated further above 4°C, it expands like a normal liquid

The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the less dense medium is 90°. When the angle of incidence exceeds the critical angle, the light ray is no longer refracted, but is instead totally internally reflected into the denser medium.

Surface tension is a property of a liquid that arises from the cohesive forces between the molecules at the surface of the liquid. These forces pull the surface molecules inward, causing the surface to behave like a stretched, elastic membrane. This effect minimizes the surface area of the liquid, which for a given volume, is a sphere

A bimetallic strip is made of two metals with different coefficients of linear expansion. When heated, the metal with the higher linear expansivity expands more than the other. This unequal expansion causes the strip to bend, with the more expansive metal on the outside of the curve. This principle is used in thermostats and thermometers

In Simple Harmonic Motion, the acceleration of the oscillating body is directly proportional to its displacement from the equilibrium position and is always directed towards that position. Therefore, the acceleration is at its maximum at the extreme positions of the oscillation, where the displacement is at its maximum

The principle of conservation of linear momentum states that in the absence of external forces, the total momentum of a system remains constant. A rocket uses this principle by expelling hot gases at high velocity in one direction. To conserve the total momentum of the rocket-gas system, the rocket itself gains momentum in the opposite direction, propelling it forward.

A fuse is a safety device used in an electrical circuit to protect it from excessive current (overcurrent). It contains a wire designed to melt and break the circuit if the current flowing through it exceeds a certain rating, thus preventing damage to appliances or the risk of fire

The half-life is the time it takes for half of the radioactive atoms in a sample to decay. In 30 years, there will have been 3 half-lives (30 years / 10 years/half-life = 3 half-lives). After the first half-life, 1/2 of the sample remains. After the second, 1/2 of that remains, which is 1/4 of the original. After the third half-life, 1/2 of the 1/4 remains, which is 1/8 of the original sample

Hypermetropia is a sight defect where the person can see distant objects clearly but cannot focus on near objects. The normal near point is 25 cm, but for a hypermetropic person, it is farther away. To correct this, a converging (convex) lens is needed to help the eye focus the light from a near object onto the retina. The lens should form a virtual image of the object at the person's near point (50 cm). Using the lens formula, $1/f = 1/u + 1/v$ , with $u = 25$ cm (desired near point) and $v = -50$ cm (virtual image at the person's near point), we have $1/f = 1/25 + 1/(-50) = 2/50 - 1/50 = 1/50$ . So, the focal length f = 50 cm = 0.5 m. The power of the lens (P) is the reciprocal of the focal length in meters: P = 1/f = 1/0.5 = +2.0 D.

A galvanometer is a type of ammeter used to detect and measure very small electric currents. It is the core component of many analog measuring instruments, and it can be converted into an ammeter or a voltmeter by adding a shunt or a multiplier resistance, respectively

The energy stored in a capacitor (E) is given by the formula $E = \frac{1}{2}CV^2$ , where $ is the capacitance and $V$ is the potential difference. The capacitance of a parallel plate capacitor is given by $C = \frac{\epsilon A}{d}$ , which is constant if the area (A) and separation ($d$) are constant. If the potential difference (V) is doubled, the new potential difference is 2V. The new energy stored will be $E_{new} = \frac{1}{2}C(2V)^2 = \frac{1}{2}C(4V^2) = 4(\frac{1}{2}CV^2) = 4E$ . Therefore, the energy stored is quadrupled.

1. Identify given values:

1. Mass (m) = 500g = 0.5 kg
2. Extension (x) = 20cm = 0.2 m
3. Final velocity (v) = 40 m/s

2. Apply Work-Energy Theorem: The work done by the catapult equals the change in kinetic energy of the stone.

1. Work Done (W) = Force (F) × Distance (x)
2. Kinetic Energy (KE) = $\frac{1}{2}mv^2$
3. Therefore, $F*X=\frac{1}{2}mv^2$

3. Substitute values and solve for F:

1. $F*0.2=\frac{1}{2}*0.5*40^2$
2. F×0.2=0.25×1600
3. F×0.2=400
4. $F=\frac{400}{0.2}=2000 N$
5. $\therefore$ F=2.0×10³ N