Question

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1. A vacuum bubble forms in a liquid and subsequently collapses. The liquid has density 1g em 3 and pressure equal to 1 standard atmosphere. The initial radius of the bubble is 2 mm. Using dimensional analysis, estimate the duration of the collapse. 2. An astronaut throws a small rock whilst standing on an open plain on Mars. Their hand is moving at approximately 60 km h - when they release the rock. The mass of Mars is approximately 11% of the mass of the Earth, the radius of Mars is approximately 53% of the radius of the Earth, and the Martian air resistance is negligible. Estimate the maximum horizontal distance that the rock can travel before hitting the ground. You may neglect the height of the astronaut. 3. A charged dust particle is at rest between the two horizontal plates of a parallel-plate capacitor. The mass and charge of the particle are known to an accuracy of 1.0%, whilst the potential difference and the distance between the plates are known to an accuracy of 0.5%. Determine the percentage accuracy to which the gravitational acceleration is known. 4. A spacecraft carrying a rescue team hurtles at relativistic speed directly towards a distant planet. A powerful on-board radio transmitter broadcasts a message at frequency 10 MHz towards the planet. Survivors on the planet shelter deep inside a long uniform metal-clad tunnel whose entrance has width 10m. Estimate the lowest speed that the spacecraft must have to ensure that the survivors can receive the message. 5. The neutron dose experienced by a human population can be estimated by measur- ing the radiation emitted by one of their coins. The coin is made of a particular metal, an atom of which, following neutron capture, forms an excited state and de- cays by emitting a y-ray photon. 2500 such photons are detected during an interval of 10%s using a 7 counter whose efficiency is 5%. Estimate the number of neutrons per unit area that must have been absorbed by the coin. The half-life of the excited state is 244.1 days and the coin has surface area 7.7 x 10-mº. 6. The difference in energy of the first excited vibrational state and the ground state of a particular diatomic molecule is approximately 19.3 meV. One of the atoms in the molecule contains 16 nucleons. By modelling the molecule as a harmonic oscillator with effective spring constant 14.5 Nm-', estimate to the nearest integer the number of nucleons in the other atom.

Answer 1

1 gm = 1x10-3 cm3 (10-273 to pa R R? 1) Given density P= 103 pressure, p= 1 atm =1.01325 pxio sp Radius, R= amm= 2x10-3n timet pb -2b T =) a fb=0 =) arab & -ab=1 & -39-b+c=0 =) ( = Bath 12/23 - 1 2 3 ta -> (795 [MI-nya (Mbey-> 30 [209 - band =29=1 = 20 = 1/2 1 =) 1/2 -1/2 Р P leto P 103 X 2x103 V 1.01325805 0.1987 ms