Physics

(a) a denser to rarer medium

Total internal reflection needs light to travel from a denser to a rarer medium with the angle of incidence greater than the critical angle.

(b) microphone

A microphone converts sound energy into electrical signals. A loudspeaker and an earphone do the reverse.

(d) equal or less than one

Displacement is never greater than the path length, so $\dfrac{|\text{average velocity}|}{\text{average speed}}=\dfrac{|\text{displacement}|}{\text{distance}}\le 1$. It equals one only for motion along a straight line without reversing.

(c) inertia

Newton's first law says a body stays at rest or in uniform motion unless acted on by an external force. This property is inertia.

(d) same as at the poles

Mass is the amount of matter in a body and does not depend on location. Only weight changes with $g$, and it becomes zero at the centre of the earth.

(c) convex mirror

A convex mirror always gives an erect, diminished image and has a wide field of view, so the driver sees more of the traffic behind.

(c) virtual and erected

A convex mirror always forms a virtual, erect and diminished image behind the mirror for any position of the object. (Option (d) is wrong because the image is diminished, not magnified.)

(d) fall down

While floating, the iron and boat together displace water equal to their weight, so the displaced volume is $W/\rho_w g$. Once the iron sinks it displaces only its own volume, which is $W/\rho_{iron}g$ and is smaller since $\rho_{iron}>\rho_w$. The total displaced volume decreases, so the water level falls.

(d) $3\times10^{8}$ m/s

All electromagnetic waves travel at $c=3\times10^{8}$ m/s in vacuum. Option (b) equals $3\times10^{9}$ m/s, so it is wrong.

(c) 20 s

Time of flight is $T=\dfrac{2u}{g}=\dfrac{2\times100}{9.8}\approx 20.4\ \text{s}\approx 20\ \text{s}$.

(c) exactly equal

In vacuum there is no air resistance, so both fall with the same acceleration $g$. From $h=\tfrac12 gt^2$, $t=\sqrt{2h/g}$, independent of mass.

(a) linear acceleration

By Newton's second law, $F=ma$, so a non-zero resultant force produces linear acceleration. Angular acceleration needs a torque.

(b) fluidity

A liquid flows and takes the shape of its container; this ability to flow is its most characteristic property.

(c) steel rod

Sound travels fastest in solids because of their high elasticity: about 5000 m/s in steel, about 1500 m/s in water and about 340 m/s in air.

(c) 440 ohm

$R=\frac{V^2}{P}=\frac{220^2}{110}=\frac{48400}{110}=440\ \Omega$

(c) conservation of linear momentum

The rocket expels gas backwards at high speed, so by conservation of linear momentum the rocket gains an equal momentum forwards.

(b) momentum

Momentum $\vec p=m\vec v$ has direction, so it is a vector. Time, volume and density are scalars.

(a) density

Pressure at depth $h$ is $P=h\rho g$, so it depends on the liquid's density (and depth and $g$), not on surface tension or viscosity.

(c) Pascal's law

Pascal's law states that pressure applied to an enclosed fluid is transmitted undiminished in all directions.

(b) pressure is greater at the bottom

Pressure in a liquid increases with depth ($P=h\rho g$), so the bottom wall must be thicker to bear the greater force.

(d) barometer

A barometer measures atmospheric pressure. A hydrometer measures density, a thermometer temperature and a calorimeter heat.

(c) remains unchanged

The floating ice displaces water of weight equal to its own weight, i.e. volume $m/\rho_w$. When it melts it becomes water of exactly that volume, so it fills the displaced space and the level does not change.

(b) 1 kg of lightly packed feather

All have the same mass, hence the same weight, but the feathers occupy the largest volume and so receive the greatest upthrust from the air. Their net weight is least, so the balloon lifts them most easily.

(d) $dgh$

Pressure in a liquid depends only on vertical height, density and $g$, not on the shape of the vessel: $P=h\,d\,g=dgh$.

(b) 10 cm

Let the side be $a$ cm (density of water $1$ g/cm³). Without the mass the cube floats with $2$ cm out, so its weight is $W=(a-2)a^2$ g. With the $200$ g mass it is just fully submerged, so $W+200=a^3$.

$200=a^3-(a-2)a^2=2a^2\Rightarrow a^2=100\Rightarrow a=10\text{ cm}$

(d) absorb sound

Concert hall walls are lined with soft, porous materials (curtains, felt, perforated panels) that absorb sound. This reduces excessive reverberation and echo so that the music is heard clearly.

(d) 800 gm

The body displaces $100$ cc of water, so it experiences an upthrust of $100$ gf. By Newton's third law the body pushes down on the water with the same force, so the reading increases by $100$ gm:

$700+100=800\text{ gm}$

(c) temperature alone

For an ideal gas there are no intermolecular forces, so the internal energy is only the kinetic energy of the molecules, $U=\tfrac{f}{2}nRT$, which depends on temperature alone (Joule's law).

(b) transverse

The prongs of a vibrating tuning fork bend sideways, perpendicular to their length, so the waves set up in the fork itself are transverse. (The sound it sends into air is longitudinal.)

(a) wavelength

The speed of sound in air increases with temperature ($v\propto\sqrt{T}$). The frequency is fixed by the source, so from $v=f\lambda$ the wavelength changes. Amplitude and intensity depend on the source and distance, not on temperature.

(c) 525 m

The successive echoes come at intervals equal to the time the sound takes to travel the distance between the two cliffs, so

$d=vt=350\times1.5=525\text{ m}$

(c) pitch of two sounds

A woman's voice has higher frequency than a man's, that is, a higher pitch. Pitch is the characteristic that distinguishes a shrill voice from a grave one.

(d) 50000 Hz

$f=\frac{v}{\lambda}=\frac{350}{7\times10^{-3}}=5\times10^{4}\text{ Hz}=50000\text{ Hz}$

(d) quality

Quality (timbre) depends on the number and relative strength of the overtones, which differ for each person. It lets us tell two voices apart even when they have the same pitch and loudness.

(b) sound intensity

The decibel (dB) is the unit of sound intensity level, $\beta=10\log_{10}(I/I_0)$ with $I_0=10^{-12}$ W/m².

(a) reflection

Reverberation is the persistence of sound in a hall after the source stops, caused by repeated reflection of sound from the walls, floor and ceiling.

(a) less absorption of sound

People and their clothes absorb sound. In an empty hall less sound is absorbed and more is reflected, so the sound seems louder (with more reverberation).

(a) centripetal acceleration

In orbit, gravity is still acting; it supplies exactly the centripetal acceleration of the spaceship and everything in it. They are in free fall together, so there is no normal reaction between a person and the floor, and the person feels weightless. $g$ is not zero at orbital height.

(b) 11.2 km/s

$v_e=\sqrt{2gR}=\sqrt{2\times9.8\times6.4\times10^6}\approx1.12\times10^{4}\text{ m/s}=11.2\text{ km/s}$

(a) 78.4 m

Starting from rest, $h=\tfrac12 gt^2=\tfrac12(9.8)(4)^2=78.4$ m. The other options ($64$ ft $\approx19.5$ m, $2000$ cm $=20$ m, $260$ m) do not match.

(a) 19.6 m

The time to reach the top is $4/2=2$ s, so

$H=ut-\tfrac12gt^2=19.6(2)-\tfrac12(9.8)(2)^2=39.2-19.6=19.6\text{ m}$

Check: $H=u^2/2g=19.6^2/19.6=19.6$ m.

(a) viscosity

The ink in a ball pen is thick and viscous. It does not leak out, but it is carried out by the rolling ball as the ball turns against the paper.

(b) longitudinal wave

In air (a gas) there is no rigidity, so sound travels as compressions and rarefactions along the direction of propagation. These are longitudinal waves.

(c) thermo electric pyrometers

Mercury boils at about $357^\circ$C and platinum resistance thermometers go up to about $1200^\circ$C. Very high temperatures, such as those of furnaces, are measured with thermoelectric (thermocouple) pyrometers.

(c) 8 cal/°C

$\text{Thermal capacity}=mc=40\times0.2=8\text{ cal/}^\circ\text{C}$

(a) 360 °C

Mercury boils at about $357^\circ$C, so a mercury thermometer can measure temperature up to about $360^\circ$C.

(a) 420

$Q=mc\Delta\theta=20\times4.2\times(15-10)=420\text{ J}$

(using $c=4.2$ J/g°C for water).