Very Short Answer Questions

No, I do not agree with Anu.
The centre of gravity of the sphere remains the same, while the centre of gravity of hollow cones and solid cones are different. The center of gravity of an object is the average position of its weight. It’s not solely determined by shape, but by how mass is distributed in that shape.

(a) His own weight causes the torque on his body and turns about his hands holding the ladder.
(b) By stretching and keeping the body parallel to the rope decreases the torque arm, reducing the torque and makes it easier to climb.

(a) In a typical car without regenerative braking, when the driver applies the brakes, the car's kinetic energy is converted into heat energy due to friction between brake pads and the wheels. This heat is then dissipated into the atmosphere and cannot be reused.

(b) Regenerative braking converts kinetic energy into electrical energy by running the electric motor in reverse, recharging the car battery.

Bottle B

Reason — Frequency is inversely proportional to the length of the air column ( $f \propto \frac{1}{l}$ ). Since pitch is directly proportional to frequency, Bottle B, having a shorter air column due to more water produces a higher frequency and therefore a higher pitch.

Surface area of bass drums is bigger than that of kettle drums. Larger the surface area louder is the sound produced.

Let resistance of wire D be R.

Resistance of wire A (R_A) = $\frac{\text R}{4}$
∵ If the diameter of a wire is doubled, the resistance becomes one-fourth of its initial value.

Resistance of wire B (R_B) = 3R
∵ If the length of a wire becomes three times its original length, the resistance becomes three times the initial resistance.

Resistance of wire C (R_C) = $\frac{\text R}{2}$
∵ If both the length and diameter of a wire are doubled, the resistance becomes half of its initial value.

Ratio of resistances = $\text{R}_\text{A} : \text{R}_\text{B} : \text{R}_\text{C} : \text{R}_\text{D} = \frac{\text R}{4}:3\text R:\frac{\text R}{2}:\text R$

Multiplying all the terms with LCM of 4 and 2 (i.e., 4) we get,

$\text{R}_\text{A} : \text{R}_\text{B} : \text{R}_\text{C} : \text{R}_\text{D} = 1 : 12 : 2 : 4$

∴ Ratio of the resistances A, B, C and D = 1 : 12 : 2 : 4

(a) We use the formula for resistance of a wire: $R = \rho \frac{L}{A}$
Where : R = resistance, $\rho$ = specific resistance (same for copper), L = length, A = cross-sectional area.

Since $\rho$ is the same for both:

$$\begin{aligned}\frac{R_1}{R_2} = \frac{\frac{L_1}{A_1}}{\frac{L_2}{A_2}} = \frac{L_1}{L_2}\frac{\cdot A_2}{\cdot A_1} \\[1em] \frac{R_1}{R_2} = \frac{1 \cdot 4}{2 \cdot 1} = \frac{4}{2} = 2:1 \\[1em]\end{aligned}$$

(b) Specific resistance (resistivity) depends only on the material, and both wires are made of copper. So, specific resistance is the same for both.
$\therefore \rho_1 : \rho_2 = 1 : 1$

(a) Convex lens, at the midpoint of the distance between the object and the image.

(b) Photocopier

Explanation:
(a) The diagram shows a real, inverted image (PQ) of the object (AB) with equal size, which gives us a strong clue that this behaviour is characteristic of a convex lens. When an object is placed at 2F (twice the focal length) from a convex lens : The image is also formed at 2F on the other side.So,

• Lens used : Convex lens
• Position of object : At 2F
• Position of lens : Exactly midway between the object (AB) and image (PQ), since both are at 2F from the lens.

(b) Photocopier / xerox machine / intermediate lens in a terrestrial telescope.

The rise in temperature is given by: ΔT = $\frac{\text{Q}}{\text{mc}}$
Where:

• Q = heat supplied (same for both)
• m = mass
• c = specific heat capacity
• Δ T = temperature change

(a) Given that masses are same,

Since: $ΔT = \frac{\text{Q}}{\text{m c}}$
here Q and m are the same for both metals A and B, so $ΔT \propto \frac{1}{\text{c}}$

So, $\frac{ΔT_A} {ΔT_B} = \frac{c_B}{c_A} =\frac{3}{2} = 3 : 2$
Metal A shows a greater temperature rise than metal B (since it has lower specific heat).

(b) Masses in ratio 3 : 5 Now :

$$\begin{aligned}\frac{ΔT_A} {ΔT_B} = \frac{m_B \cdot c_B}{m_A\cdot c_A} \\[1em] \frac{ΔT_A} {ΔT_B} = \frac{5 \cdot 3}{3 \cdot 2} \\[1em] \frac{ΔT_A} {ΔT_B} = \frac{15}{6} \\[1em] \frac{ΔT_A} {ΔT_B} = \frac{5}{2} \\[1em] \\[1em] {ΔT_A} :{ΔT_B} =5 : 2\end{aligned}$$

The ratio of temperature rise is 5 : 2

Let same vertical height of cone be h.

In a right circular cone, the center of gravity lies at a distance of $\frac{h}{4}$ from the base for a solid cone, and at a distance of $\frac{h}{3}$ from the base for a hollow cone.

Given that the difference between these positions is 1.5 cm, we can set up the following equation:

$$\begin{aligned}\frac{h}{3} - \frac{h}{4} = 1.5 \\[1em] \frac{4h-3h}{12} = \frac{3}{2}\\[1em] \frac{h}{12}= \frac{3}{2}\\[1em] h= \frac{36}{2}\\[1em] h= 18 \text{ cm} \\[1em]\end{aligned}$$

∴ The vertical height of each cone = 18 cm

Natural frequency of a body is inversely proportional to the length of the body. High frequency seismic waves can resonate with short length buildings, and due to the large amplitude of vibration, it can cause more damage to the buildings.

No.

Reason

• Mercury is denser than oil—about 13.6 times as dense. If filled horizontally, meaning mercury and oil are layered due to gravity, Mercury will settle at the bottom, oil will float above. This creates an asymmetrical mass distribution, with heavier mass concentrated towards the bottom.
• The centre of gravity will shift towards the mercury side as the position of the centre of gravity depends on the distribution of mass.

(a) Worker is attempting to lower the load.

(b) For rotational equilibrium about the fulcrum,

Clockwise Moment = Anticlockwise Moment

Assuming 1 kgf ≈ 9.8 N, we convert W₁ = 4000 kgf ≈ 4000 x 9.8 = 39,200 N

• Moment due to Load (anticlockwise) :
  M₁ = W₁ d₁ = 39,200 x 25 = 980,000 Nm
• Moment due to Worker’s Force (clockwise) :
  M₂ = F₂ x d₂ = 20,000 x 10 = 200,000 Nm

The clockwise moment (200,000 Nm) is much less than the anticlockwise moment (980,000 Nm). Their applied force is insufficient to raise the load, so that worker will lower the load.

(a) Slope

(b) 2nd class

Explanation:

(a) The slope of the load-effort graph is the key to finding mechanical advantage.

(b) In a linear load-effort graph that passes through the origin, the slope represents the ratio of Load to Effort. So, we just need to calculate the slope of the line to get the mechanical advantage. Choose any point on the line — for instance, (Effort = 10 kgf, Load = 20 kgf) gives MA = 2.
Since MA > 1, meaning effort arm > load arm. This is characteristic of a class II lever, where the load lies between the fulcrum and the effort.

(a) 1 J/g °F = 1800 J / (kg K)

(b) 336J of energy is used to increase the potential energy due to an increase in intermolecular separation, so the latent heat of ice is 336 J.

Explanation:

(a) ∵ 1 gram = 0.001 kg

$\because 1 °F = \frac{5}{9} K$

Now convert: $$\begin{aligned}1~\text{J}/{\text{g °F}} \\[1em] = \frac{1\text{J}}{0.001 \text{kg} \times \frac{5}{9} , \text{K}} \\[1em] = \frac{1}{0.001 \times \frac{5}{9}} ~~\text{J/(kg K)}\\[1em] = \frac{9}{0.005} = 1800~ \text{J/(kg K)}\end{aligned}$$

(b) At 0 °C, ice and water are at the same temperature, but not at the same energy state. To convert 1 g of ice at 0 °C into 1 g of water at 0 °C, it must absorb latent heat.

This latent heat of fusion for water is: L_f = 336 J/g

So, to melt 1 g of ice: Q = mL = 1 g x 336 J/g = 336 J

Thus, 1 g of water at 0 °C has 336 J more energy than ice at the same temperature because that’s the energy absorbed during the phase change.

(i) - (c)

(ii) - (a)

Explanation:

(i) (c) : class I lever

• Nodding head : In this action, the spine acts as the fulcrum F, load L is at its front part, while effort E is at its rear part. Since the fulcrum is between load and effort, Thus, this is an example of class I lever.
• See-Saw : Since the fulcrum is between load and effort, the see-saw satisfies the condition for a class I lever.

(ii) (a) : class II lever

• Lifting body weight on your toes: the weight of the body is raised on toes. The fulcrum F is at the toes at one end, the load L (i.e., weight of the body) is in the middle and effort E by muscles is at the other end. Thus, this is an example of class II lever.
• Bottle Opener: Now let’s map this to a bottle opener in action:

The load is positioned between the fulcrum and the effort. Thus, this is an example of class II lever.

In socket, the upper bigger hole is for earth connection, while the hole on the right side is for connection to the live wire and the hole on the left side is for connection to the neutral wire of the electric supply.

Placing the phone in a steel glass amplifies the sound due to a few reasons:

• Resonance Effect: The air column inside the glass has same natural frequency for certain frequencies produced by phone speaker, due to resonance its loudness increases.
• When we put our phone in a glass, the sound from the speaker makes the glass vibrate. The glass has more surface area than the phone speaker alone, so it vibrates more air. More moving air means stronger sound waves, and that makes the sound feel louder to our ears.

Given,
Number of resistors = 3
Resistance of each resistor, R = 3 Ω

(a) To get maximum equivalent resistance: Connect all in series combination, resistances simply add:

$\text{R}_{\text s} = \text{R} + \text{R} + \text{R} = 3 + 3 + 3 = 9 Ω$

This is the maximum possible equivalent resistance using all three.

(b) To get minimum equivalent resistance: connect all in parallel combination.

By the reciprocal formula:

$$\begin{aligned}\frac{1}{R_{\text p}} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} \\[1em] \frac{1}{R_{\text p}}= \frac{1}{3} + \frac{1}{3} + \frac{1}{3} \\[1em] \frac{1}{R_{\text p}}= \frac{3}{3} \\[1em] \\[1em] R_{\text p} = \frac{3}{3} = 1 Ω\end{aligned}$$

This gives the minimum possible equivalent resistance.

(a) The force responsible for keeping the electron in its circular orbit around the nucleus is the: Electrostatic (Coulomb) Force

(b) According to Newton's First Law, in the absence of a centripetal (electrostatic) force, an electron would not maintain circular motion and would move in a straight line tangential to its instantaneous velocity.

(a) When current flows upward through the vertical wire, it creates a circular magnetic field around the wire (as per right-hand thumb rule). The iron filings are tiny magnets in the presence of magnetic field and they align themselves along these field lines, forming concentric circles.

(b) The concentration of magnetic field lines will increase/the number of concentric circles will increase up to a greater distance.

Ice is added to warm water on a hot summer day because it absorbs heat from the water to melt. This happens due to the latent heat of fusion, which is 336 J/g, the amount of energy required to change ice from solid to liquid without a rise in temperature. As ice absorbs this heat, the water loses energy, leading to a drop in its temperature and making it cooler.

No, voltmeter is a high-resistance device. Ideally, its resistance is infinite. So, if by mistake, the ammeter is replaced by the voltmeter, the total resistance of the circuit will also become infinite. In that case, the current flowing through the circuit will become almost zero, and the circuit will not work properly.

Given,
Length of the rod = 1 meter or 100 cm
Mass of copper part = m₁ = 900 g
Mass of iron part = m₂ = 800 g

The copper part is 50 cm long and its center of gravity will be at 25 cm.

The iron part is also 50 cm long and its center of gravity will be at 75 cm.
Then distance between their CG is = (75 - 25) cm = 50 cm.

Let x be the distance of CG of copper part from pivot, then (50 - x) will be the distance of CG of iron part from pivot.

900 x = 800 (50-x)
900 x = 40000−800 x
1700 x = 40000

$\text x=\frac{40000}{1700}$

x = 23.53 cm

So, the metre rod will be balanced at a distance (25 + 23.53) cm = 48.53 cm from the end of copper.

Compass P will show prominent deflection.
The magnetic field induced by the current in compass P, when added to Earth's magnetic field, will result in a stronger magnetic field above the wire.
The magnetic field induced by the current in compass Q is opposite to Earth's magnetic field, will result in a weaker magnetic field below the wire, depending on the given current's direction.

Let mass of water = m
Height of water fall = h
Change in temperature = Δt

Given that specific heat capacity of water (s)= 4200 J kg^-1 °C^-1 and g = 10 N kg^-1

The potential energy of water at the top of the waterfall is converted into heat as the water falls.

∴ mgh = msΔt
10 h = 4200 x 0.2

h = $\frac{840}{10}$

h = 84 m

Hence, height of water fall is 84 m.

(a) The surface of the glass with water is curved so it acts like a convex lens. Thus, due to the refraction through a convex lens it appears bigger (thicker).

(b) Due to refraction, when light passes through water, lateral displacement takes place which shifts the position of the image and makes it appear discontinuous.

(a) Point Q

(b) S, R

Both points S and R are possible because the bending of light depends on several factors such as the medium’s refractive index, the angle of incidence, and the wavelength of light.