Question:
An object requires 500 N force to be pulled up on a \(30^\circ\) frictionless smooth inclined plane at a constant speed. Determine the weight of the object.
An object requires 500 N force to be pulled up on a \(30^\circ\) frictionless smooth inclined plane at a constant speed. Determine the weight of the object.
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For objects moving at constant speed on a frictionless incline, applied force equals the component of weight along the incline: \(F = W \sin \theta\).
Updated On: Jul 18, 2026
- \(500\sqrt{2} \, \text{N}\)
- \(1000 \, \text{N}\)
- \(1000\sqrt{2} \, \text{N}\)
- \(500\sqrt{3} \, \text{N}\)
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The Correct Option is B
Solution and Explanation
Step 1: Analyze the forces on the inclined plane.
On a frictionless inclined plane, pulling an object at constant speed means net acceleration is zero. Therefore, the applied force \(F\) balances the component of weight along the incline:
\[ F = W \sin \theta \]
Step 2: Identify known quantities.
Given: \(F = 500 \, \text{N}\), \(\theta = 30^\circ\). Unknown: weight \(W\).
Step 3: Write equation for weight.
\[ W = \frac{F}{\sin \theta} \]
Step 4: Substitute values.
\[ W = \frac{500}{\sin 30^\circ} = \frac{500}{0.5} = 1000 \, \text{N} \]
Step 5: Verify reasoning.
Since the plane is frictionless and motion is at constant speed, only the component of weight along incline matters. Calculation matches given conditions.
Step 6: Final conclusion.
Thus, the weight of the object is:
\[ \boxed{1000 \, \text{N}} \]
On a frictionless inclined plane, pulling an object at constant speed means net acceleration is zero. Therefore, the applied force \(F\) balances the component of weight along the incline:
\[ F = W \sin \theta \]
Step 2: Identify known quantities.
Given: \(F = 500 \, \text{N}\), \(\theta = 30^\circ\). Unknown: weight \(W\).
Step 3: Write equation for weight.
\[ W = \frac{F}{\sin \theta} \]
Step 4: Substitute values.
\[ W = \frac{500}{\sin 30^\circ} = \frac{500}{0.5} = 1000 \, \text{N} \]
Step 5: Verify reasoning.
Since the plane is frictionless and motion is at constant speed, only the component of weight along incline matters. Calculation matches given conditions.
Step 6: Final conclusion.
Thus, the weight of the object is:
\[ \boxed{1000 \, \text{N}} \]
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