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Force to push a block up an incline versus force to stop it sliding down

This type of question, asked 2 times: 25 Jan 2023, 31 Jan 2024. All 2 questions below, oldest first.

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  1. Question 1

    25 Jan 2023

    100
    Consider a block kept on an inclined plane (inclined at 45∘45^{\circ} ) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane (μ)(\mu) is equal to:

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  2. Question 2

    31 Jan 2024

    102
    A block of mass 5 kg5\text{ }kg is placed on a rough inclined surface as shown in the figure. If F→1{\overrightarrow{F}}_{1} is the force required to just move the block up the inclined plane and F→2{\overrightarrow{F}}_{2} is the force required to just prevent the block from sliding down, then the value of ∣F→1∣−∣F→2∣\left| {\overrightarrow{F}}_{1} \right|-\left| {\overrightarrow{F}}_{2} \right| is: [Use  g=10 m/s2]\left. \ g = 10\text{ }m/s^{2} \right\rbrack

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