Question

Two different syringes having radii in the ratio 1: 5 are applied with same pressure. The forces acting on these syringes are in the ratio

• A. 5:1
• B. 1:10
• C. 1:25
• D. 25:1
• E. 1:5

Hint:

Force is proportional to the square of the radius when pressure is constant.

Answer 1

The Correct Option is C

Step 1: Concept
Pressure ($P$) is defined as Force ($F$) divided by Area ($A$): $P = F/A$.

Step 2: Meaning
If pressure is the same, then $F \propto A$. For a circular syringe, Area $A = \pi r^2$.

Step 3: Analysis
$F_1/F_2 = A_1/A_2 = (r_1/r_2)^2 = (1/5)^2 = 1/25$.

Step 4: Conclusion
Hence, the forces acting are in the ratio 1:25.
Final Answer: (C)