Step 1: Identify the pattern.
The series alternates between division and multiplication:
- \( 8 \div 2 = 4 \)
- \( 4 \times 1 = 4 \)
- \( 4 \times 1.5 = 6 \)
- \( 6 \times 2 = 12 \)
Following this pattern, we multiply 12 by 2.5:
\[
12 \times 2.5 = 30
\]
Final Answer: \[ \boxed{30} \]
What comes next in the series?
\(2, 6, 12, 20, 30, \ ?\)
A weight of $500\,$N is held on a smooth plane inclined at $30^\circ$ to the horizontal by a force $P$ acting at $30^\circ$ to the inclined plane as shown. Then the value of force $P$ is:
A steel wire of $20$ mm diameter is bent into a circular shape of $10$ m radius. If modulus of elasticity of wire is $2\times10^{5}\ \text{N/mm}^2$, then the maximum bending stress induced in wire is: