1. (d) Between the pole of the
mirror and its principal focus (Review: Concave mirror forms virtual,
erect, magnified image ONLY when object is within focal length.)
2. (c) Ciliary muscles
3. (c) 2A ($R = \rho l/A$. For new wire $R' = R$, length $2l$. So $\rho(2l)/A' = \rho l/A
\implies A' = 2A$.)
4. (d) Is the same at all
points (Inside a long solenoid, field is uniform.)
5. (b) IR2 ($P = VI = I^2R = V^2/R$. $IR^2$ is incorrect.)
6. (b) Is scattered the least by
smoke or fog (Rayleigh scattering $\propto 1/\lambda^4$. Red has
longest wavelength, so least scattered.)
7. (b) R1 >
R2 > R3 (Slope of V-I graph $= V/I = R$. $R_1$
has steepest slope.)
8. (c) Producing induced current in
a coil due to relative motion
9. (b) i > r (Light travels from rare (air) to denser (glass) medium, bends towards
normal.)
10. (b) 3.6 × 106
J
11. (d) Heating effect of
current
12. (a) Light is least
scattered (Sun is overhead, light travels shorter distance, less
scattering of blue.)
13. (d) All of these
14. (d) All mirrors irrespective of
their shape
15. (b) Same current flowing
through them when connected in series
16. (b) A convex mirror
(Always forms diminished, erect image with wide field of view.)
17. (c) The shape of the resistor
is changed (Resistivity depends only on material and temperature, not
dimensions.)
18. (b) 1/25 Ω (For minimum resistance, connect in parallel: $R_{eq} = R/n = (1/5)/5 =
1/25$.)
19. (c) Behind the retina
20. (c) Originate from the North
Pole and end at its South Pole
21.
(a) Definition: It is the reciprocal of focal length (in meters). $P = 1/f$.
(b) SI Unit: Dioptre (D).
(c) Calculation: For concave lens, $f = -2$ m.
$P = 1/(-2) = -0.5$ D.
22.
At high altitudes where astronauts exist, there is no atmosphere to scatter light. Since there is no
scattering of light, no light reaches the eye from the surroundings, and hence the sky appears dark
(black) instead of blue.
23.
1. Length ($l$): Resistance is directly proportional to length ($R \propto l$).
2. Area of cross-section ($A$): Resistance is inversely proportional to area ($R
\propto 1/A$).
(Note: Nature of material and temperature are also factors.)
24.
Diagram Check: Lines should emerge from North Pole and merge at South Pole externally.
Internally they go from South to North. Lines should form closed loops and not intersect.
25.
Resistance ($R$): $R = V^2/P = 220^2 / 100 = 48400 / 100 = 484 \Omega$.
New Power ($P'$): When $V' = 110$ V.
$P' = (V')^2 / R = 110^2 / 484 = 12100 / 484 = 25$ W.
Answer: 25 Watts.
26.
Given: $h_o = 5$ cm, $u = -25$ cm, $f = +10$ cm (Convex Lens).
Lens Formula: $1/f = 1/v - 1/u \implies 1/v = 1/f + 1/u = 1/10 - 1/25$.
$1/v = (5-2)/50 = 3/50$. So, $v = 50/3 = +16.67$ cm.
Magnification ($m$): $m = v/u = (50/3) / (-25) = -2/3 = -0.67$.
Size of Image ($h_i$): $h_i = m \times h_o = -2/3 \times 5 = -3.33$ cm.
Nature: Real, Inverted, Diminished.
27.
Joule's Law: Heat produced in a resistor is directly proportional to:
(i) Square of current ($I^2$), (ii) Resistance ($R$), and (iii) Time ($t$). $H = I^2Rt$.
Devices: Electric Heater, Electric Iron, Electric Geyser, Fuse.
28.
Formation: Rainbow is caused by dispersion, refraction, and internal
reflection of sunlight by tiny water droplets present in the atmosphere.
Sequence: 1. Sunlight enters droplet (Refraction + Dispersion). 2. Internal Reflection
at back of droplet. 3. Refraction again as it exits droplet.
Diagram: Should show light entering drop, splitting, reflecting internally, and
emerging as spectrum (Red on top, Violet at bottom).
29.
Power Additive in Parallel? No, current is additive.
Current $I_1$ (100W) = $P_1/V = 100/220 = 5/11$ A ($0.45$ A).
Current $I_2$ (60W) = $P_2/V = 60/220 = 3/11$ A ($0.27$ A).
Total Current ($I$): $I = I_1 + I_2 = (100+60)/220 = 160/220 = 8/11$ A $\approx 0.73$
A.
30.
Properties: 1. Originate N pole, terminate S pole. 2. Continuous closed curves. 3.
Tangent gives direction. 4. Closer lines = stronger field.
No Intersection: If two lines intersected, at the point of intersection there would be
two tangents representing two directions of magnetic field, which is impossible.
31.
Person can see distinctly only beyond 50 cm. Near point has receded from 25 cm to 50 cm.
(a) Defect: Hypermetropia (Far-sightedness).
(b) Reasons: Focal length of eye lens is too long OR eyeball has become too small.
(c) Calculation: Object placed at normal near point ($u = -25$ cm) should form virtual
image at defective near point ($v = -50$ cm).
$1/f = 1/v - 1/u = 1/(-50) - 1/(-25) = -1/50 + 2/50 = 1/50$.
$f = +50$ cm $= +0.5$ m.
$P = 1/f = 1/0.5 = +2.0$ D.
Nature: Convex Lens.
32.
(a) Derivation for Parallel:
- Current $I$ splits into $I_1, I_2, I_3$. Total $I = I_1 + I_2 + I_3$.
- Voltage $V$ is same across all.
- From Ohm’s law: $I_1 = V/R_1, I_2 = V/R_2, I_3 = V/R_3$.
- Equivalent circuit: $I = V/R_{eq}$.
- $V/R_{eq} = V/R_1 + V/R_2 + V/R_3$.
- $1/R_{eq} = 1/R_1 + 1/R_2 + 1/R_3$.
(b) Calculations (Based on Diagram):
Given: $R_1=5\Omega, R_2=10\Omega, R_3=30\Omega, V=12\text{V}$.
(i) Current through each:
$I_1 = V/R_1 = 12/5 = \mathbf{2.4\text{ A}}$.
$I_2 = V/R_2 = 12/10 = \mathbf{1.2\text{ A}}$.
$I_3 = V/R_3 = 12/30 = \mathbf{0.4\text{ A}}$.
(ii) Total Current: $I = 2.4 + 1.2 + 0.4 = \mathbf{4.0\text{ A}}$.
(iii) Total Resistance: $R = V/I = 12/4 = \mathbf{3\Omega}$.
(Verification: $1/R = 1/5 + 1/10 + 1/30 = (6+3+1)/30 = 10/30 = 1/3 \implies R=3$.)
33.
(a) Laws of Refraction: (i) Incident ray, refracted ray, normal all lie in same plane.
(ii) Ratio of sine of angle of incidence to sine of angle of refraction is constant (Snell's Law: $\sin
i / \sin r = n$).
(b) Diamond (n=2.42): It means the speed of light in diamond is $1/2.42$ times the
speed of light in vacuum (It travels very slowly).
(c) Ray Diagram: Object between Pole (P) and Focus (F) of Concave Mirror.
- Ray parallel to axis passes through F.
- Ray through C retraces path.
- Rays diverge in front, appear to meet behind mirror.
Characteristics: Virtual, Erect, Magnified.
34.
(a) Solenoid: A coil of many circular turns of insulated copper wire wrapped closely in
the shape of a cylinder. Pattern resembles a bar magnet (uniform inside, curved loops outside).
(b) Fleming's Left-Hand Rule: Stretch thumb, forefinger, and central finger of left
hand mutually perpendicular. Forefinger = Field (B), Center Finger = Current (I), Thumb = Force (F).
(c) Direction of Force:
- Field (B): Right.
- Motion of Electron: Down.
- Current (I): Opposite to electron motion => UP.
- Apply Rule: Forefinger Right, Center Finger Up => Thumb points Into the Page.
35.
(a) Power of Accommodation: The ability of the eye lens to adjust its focal length to
see both near and distant objects clearly.
(b) Correction: Person cannot see far objects (Myopia). Needs a Concave
Lens.
Calculation (optional but good): $u = \infty, v = -1.2\text{m}$. $P = 1/(-1.2) = -0.83$ D.
(c) Diagrams:
(i) Myopic Eye: Image forms in front of retina.
(ii) Correction: Concave lens diverges rays so they focus ON retina.
36.
(i) Convex mirrors give an erect (upright) image and have a
wider field of view (curved outwards), allowing driver to see large area.
(ii) $R = +3.00$ m. $f = R/2 = +1.50$ m.
(iii) $u = -5.00$ m, $f = +1.50$ m.
$1/v = 1/f - 1/u = 1/1.5 - 1/(-5) = 10/15 + 1/5 = 2/3 + 1/5 = (10+3)/15 = 13/15$.
$v = 15/13 \approx +1.15$ m.
Image is formed $1.15$ m behind the mirror. Virtual, Erect, Diminished ($m = -v/u =
-1.15/-5 = +0.23$).
37.
(i) Earth Wire: It provides a low-resistance path for leakage current to flow to the
earth, preventing electric shock to the user in case of insulation failure.
(ii) Parallel Connection: (a) Each appliance gets full voltage (220V). (b) If one
appliance fails, others continue to work. (c) Separate switches possible.
(iii) Overloading:
Power $P = 2$ kW $= 2000$ W. Voltage $V = 220$ V.
Current drawn $I = P/V = 2000/220 \approx 9.09$ A.
Since current ($9.09$ A) exceeds the rating ($5$ A), the fuse wire will melt or circuit will break
(Overloading).
38.
(i) Bends Least: Red.
(ii) Bends Most: Violet.
(iii) Newton's Experiment: He placed a second identical glass prism in an
inverted position with respect to the first prism. The dispersed colors from the first
prism recombined in the second prism to emerge as a beam of white light.
