A block of √3 kg is attached to a string whose other end is attached to the wall. An unknown force F is applied so that the string makes an angle of 30° with the wall. The tension T is: (Given g=10 ms⁻² )

Solution

Physics sir · 3 steps

Work at the knot: F is horizontal, so only T can hold up the weight vertically.

1. Forces at the knot. Three forces act at the point where the strings meet. The lower string pulls down with the weight mg = √3 × 10 = 10√3 N. F pulls horizontally. T pulls up along the string, at 30° to the vertical wall.
2. Balance vertically. F has no vertical part. So the vertical component of T, which is T cos 30° because the angle is measured from the vertical, must balance the weight on its own.

   T cos 30° = mg ⇒ T × √3/2 = 10√3

3. So. T = 20 N, which is option (d). As a check, the horizontal balance gives F = T sin 30° = 10 N.

The idea to keep. In a string-junction problem, balance along the direction where only one unknown force has a component. If the angle is from the vertical, the vertical part is the cosine.

Answer from the NTA final answer key. Solution by PrepWiser.