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Question:
A block of mass 5 kg is placed on a rough inclined surface as shown in the figure.
If \(\vec{F_1}\) is the force required to just move the block up the inclined plane and \(\vec{F_2}\) is the force required to just prevent the block from sliding down, then the value of \(|\vec{F_1}| - |\vec{F_2}|\) is: [Use \(g = 10 \, \text{m/s}^2\)]
A block of mass 5 kg is placed on a rough inclined surface as shown in the figure.
If \(\vec{F_1}\) is the force required to just move the block up the inclined plane and \(\vec{F_2}\) is the force required to just prevent the block from sliding down, then the value of \(|\vec{F_1}| - |\vec{F_2}|\) is: [Use \(g = 10 \, \text{m/s}^2\)]
If \(\vec{F_1}\) is the force required to just move the block up the inclined plane and \(\vec{F_2}\) is the force required to just prevent the block from sliding down, then the value of \(|\vec{F_1}| - |\vec{F_2}|\) is: [Use \(g = 10 \, \text{m/s}^2\)]
Updated On: Nov 19, 2024
- \(25 \sqrt{3} \, \text{N}\)
- \(5\sqrt{3} \, \text{N}\)
- \(\frac{5 \sqrt{3}}{2} \, \text{N}\)
- \(10 \, \text{N}\)
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The Correct Option is B
Solution and Explanation
The block experiences frictional force due to the roughness of the inclined surface. The kinetic friction force \( f_k \) is given by:
\[ f_k = \mu mg \cos \theta, \]where \( \mu = 0.1 \) is the coefficient of friction, \( m = 5 \, \text{kg} \), and \( \theta = 30^\circ \).
Calculating \( f_k \):
\[ f_k = 0.1 \times 5 \times 10 \times \cos 30^\circ = 0.1 \times 50 \times \frac{\sqrt{3}}{2} = 2.5 \sqrt{3} \, \text{N}. \]To move the block up the incline, the force \( F_1 \) must overcome both the component of gravitational force along the incline and the frictional force. Therefore:
\[ F_1 = mg \sin \theta + f_k. \]Substitute the values:
\[ F_1 = 5 \times 10 \times \sin 30^\circ + 2.5 \sqrt{3} = 25 + 2.5 \sqrt{3} \, \text{N}. \]To prevent the block from sliding down, the force \( F_2 \) must balance the component of gravitational force along the incline, reduced by the frictional force. Thus:
\[ F_2 = mg \sin \theta - f_k. \]Substitute the values:
\[ F_2 = 25 - 2.5 \sqrt{3} \, \text{N}. \]The difference \( |F_1 - F_2| \) is:
\[ |F_1 - F_2| = |(25 + 2.5 \sqrt{3}) - (25 - 2.5 \sqrt{3})| = 5 \sqrt{3} \, \text{N}. \]Thus, the answer is:
\[ 5 \sqrt{3} \, \text{N}. \]Was this answer helpful?
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