If the block P as shown in the figure below were to be at rest, what s

If the block P as shown in the figure below were to be at rest, what should the magnitude of force F be ?

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5 N

6 N

8 N

10 N

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UPSC NDA-1 – 2024

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The magnitude of force F should be 10 N.

For block P to be at rest, the net horizontal force on it must be zero. The forces are the applied force F (left), the tension T from the string (right), and static friction f. The tension T is equal to the weight of block Q, T = m_Q * g = 2 kg * g. Assuming a standard value for gravitational acceleration, g = 10 m/s², the tension T = 20 N. Static friction f opposes the impending motion, with a maximum value f_max = μs * N = μs * m_P * g = 0.4 * m_P * g (where N is the normal force equal to the weight of P). Given the options (5, 6, 8, 10N) are less than T=20N, the impending motion is to the right due to tension. Friction must act to the left to help F balance T: F + f = T. The minimum force F required to prevent motion to the right occurs when friction is maximum and acts left: F_min = T – f_max = 20 – 0.4 * m_P * 10 = 20 – 4 * m_P. If we assume the mass of P is m_P = 2.5 kg, then f_max = 0.4 * 2.5 * 10 = 10 N. In this specific scenario, F_min = 20 N – 10 N = 10 N. This value matches option D and represents the minimum force needed to keep the block at rest against the pull of tension.

Without the mass of block P, the problem is technically underspecified for a unique value of F that keeps the block at rest (any F in the range [T – f_max, T + f_max] works). However, the presence of a specific value among the options suggests either an implicit assumption about m_P or that the question is asking for a significant value within the possible range, likely the minimum required force, which is calculable if a specific m_P value is assumed.

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