Physics

(d) all of the above X-rays are high-energy electromagnetic radiation of very short wavelength, and they are absorbed by dense metals such as lead, which is why lead shielding is used.

(d) all Heat can raise the temperature of a body, increase its volume (thermal expansion) and change its state (melting, boiling).

(c) $\le 1$

Displacement is the shortest (straight-line) distance between the start and end points, while distance is the actual path length. So displacement $\le$ distance, and the ratio is $\frac{\text{displacement}}{\text{distance}} \le 1,$ with equality only for motion along a straight line without reversing.

(d) 74.6 N

At uniform velocity the engine force equals the friction force, and $P = Fv$. With $P = 1\ \text{HP} = 746$ W: $F = \frac{P}{v} = \frac{746}{10} = 74.6\ \text{N}$

(b) 0

At the centre of the earth the net gravitational pull from the surrounding mass cancels in all directions, so $g = 0$ and the weight $mg = 0$.

(b) $gR^2/G$

At the surface $g = \dfrac{GM}{R^2}$, so $M = \frac{gR^2}{G}$

(a) decreases

An immersed body experiences an upward buoyant force, so apparent weight = actual weight $-$ upthrust, which is less than the actual weight.

(c) frequency decreases

The speed of sound in air depends on the medium: it rises with temperature and with humidity (so it falls when temperature or humidity decreases), but it does not depend on frequency ($v = f\lambda$, and $\lambda$ adjusts). So lowering the frequency does not decrease the velocity.

(a) 24

For diamond, $n \approx 2.42$: $\sin C = \frac{1}{n} = \frac{1}{2.42} \approx 0.413 \Rightarrow C \approx 24.4^\circ \approx 24^\circ$

(a) $8.4 \times 10^3$

Thermal capacity $= mc = 2 \times 4200 = 8400\ \text{J/}^\circ\text{C} = 8.4 \times 10^3$ J/°C, using $c = 4200$ J/kg°C for water.

(d) length

A light year is the distance light travels in one year, about $9.46 \times 10^{15}$ m.

(c) acceleration

Weight $W = mg$, so it changes when the acceleration due to gravity $g$ changes (for example with altitude or place), while the mass stays constant.