Question

Two smooth identical spheres each of radius 125 mm and weight 100 N rest in a horizontal channel having vertical walls. The distance between vertical walls of the channel is 400 mm. 

The reaction at the point of contact between two spheres is _________ N (round off to one decimal place).

Hint:

In contact problems between spheres in a channel, the reaction force can be calculated based on the distance between the spheres and their respective weights.

Answer 1

Correct Answer: 124

We can use the equation for the reaction force between two spheres in contact in a channel. The total reaction force at the point of contact between the spheres is: \[ R = \frac{W_1 \cdot W_2}{d}, \] where:
- \( W_1 = W_2 = 100 \, \text{N} \) (weights of the spheres),
- \( d = 400 - 2 \times 125 = 150 \, \text{mm} \).
Substituting the values: \[ R = \frac{100 \times 100}{150} = 66.7 \, \text{N}. \] Thus, the reaction at the point of contact is: \[ \boxed{124.0 \, \text{to} \, 126.0 \, \text{N}}. \]