Live practice

A steel shaft has diameter \(8.70\,\mathrm{cm}\) at 27°C, while the wheel hole is \(8.69\,\mathrm{cm}\). To what temperature must the shaft be cooled? α=1.20×10⁻⁵ K⁻¹.

Four hollow steel columns support 50,\(000\,\mathrm{kg}\) uniformly. Each has outer radius \(0.60\,\mathrm{m}\) and inner radius \(0.30\,\mathrm{m}\). Find compressive strain using Y=2.0×10¹¹ Pa and \(g=9.8\,\mathrm{m\,s}\)⁻².

Does escape speed from Earth depend on projectile mass, launch location, launch direction, or launch height?

Perpendicular forces of 8 N and 6 N act on a \(5\,\mathrm{kg}\) body. Find the acceleration magnitude and direction.

For class intervals 0–10, 10–20, 20–30 with frequencies 3,5,2, calculate the mean.

Find the point dividing the segment from A(1,2,3) to B(6,7,8) internally in the ratio 2:3.

A directed line is turned 30° anticlockwise from the positive y-axis. Find its slope.

For aₙ=4n−3, calculate a₁₇ and a₂₄.

Evaluate 102⁵ using the binomial theorem.

Evaluate (i) 8!(ii) 4!−3!.