Physics

(c) 3.5

The question refers to a simple magnifying lens of focal length $f = 10$ cm, with the image at the near point $D = 25$ cm:

$M = 1 + \frac{D}{f} = 1 + \frac{25}{10} = 3.5$

(a) Acceleration

Since $a = \dfrac{dv}{dt}$, the slope of a velocity-time graph is the acceleration. The area under it gives displacement.

(a) Constant velocity

By Newton's first law, a body moving with constant velocity has zero acceleration, so the net force is zero. Circular motion, constant acceleration and variable acceleration all need a net force.

(b) 125%

For a bulb of fixed resistance, $P = V^2/R$, so $P \propto V^2$.

$\frac{P_2}{P_1} = (1.5)^2 = 2.25$

The power increases by $2.25 - 1 = 1.25$, that is, 125%.

(d) Different overtone is present in them

Quality (timbre) distinguishes two sounds of the same pitch and loudness. It depends on the number and relative intensities of the overtones (harmonics) present in the waveform.

(c) Diffraction

Radio waves have wavelengths of metres, comparable to the size of doors and windows, so they diffract and bend into a closed room. Light has a wavelength of about $5\times10^{-7}$ m, far smaller than the openings, so diffraction is negligible and it does not reach inside.

(b) 7250

Taking ice at $-10^\circ$C converted to steam at $100^\circ$C ($c_{ice}=0.5$, $L_f=80$, $c_w=1$, $L_v=540$ cal/g):

$Q = 10(0.5)(10) + 10(80) + 10(1)(100) + 10(540) = 50 + 800 + 1000 + 5400 = 7250 \text{ cal}$

(Heating the steam a further 10 degrees would add only about 50 cal; the listed option is 7250.)

(c) energy

Lenz's law says the induced current opposes the change causing it. If it aided the change, energy would be created from nothing, so the law follows from conservation of energy.

(d) inertia

Inductance opposes any change in current, as mass opposes change in velocity. The magnetic energy $\tfrac12 LI^2$ corresponds to kinetic energy $\tfrac12 mv^2$, so $L$ is the electrical analogue of mass (inertia).