Q4. Using NCERT’s values for rock (elastic limit 30 × 10 N m, density 3 × 10 kg m), estimate the greatest height of a mountain on Mars, where g is about 3.7 m s.
h = 30 × 10/(3 × 10 × 3.7), about 2.7 × 10 m, roughly 27 km. With weaker gravity, mountains can be far taller than on the Earth.
Q5. A steel wire must hang a 500 kg load with a safety factor of five in the load. Taking steel’s yield strength as 250 × 10 N m (NCERT Table 8.1) and g = 9.8 m s, find the least radius.
A = 5 × 500 × 9.8/(250 × 10) = 9.8 × 10 m, so r = √(A/π), about 5.6 × 10 m, or 5.6 mm.
Q6. By what percentage does the sag of a beam fall if its depth is increased by 20%, everything else unchanged?
δ ∝ 1/d, so the new sag is 1/1.2 ≈ 0.579 of the old one: about 42% less.