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Two masses 5 kg and 3 kg are suspended f...

Two masses 5 kg and 3 kg are suspended from the ends of an unstretchable light string passing over a frictionless pulley. When the masses are released, the thrust on the pulley is (g = `10 ms^(-2)`)

A

80 N

B

37.5 N

C

150 N

D

75 N

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of finding the thrust on the pulley when two masses (5 kg and 3 kg) are suspended from a light string over a frictionless pulley, we can follow these steps: ### Step 1: Identify the Forces Acting on Each Mass - For the 3 kg mass, the weight acting downwards is \( W_1 = 3g \). - For the 5 kg mass, the weight acting downwards is \( W_2 = 5g \). - The tension in the string is denoted as \( T \). ### Step 2: Write the Equations of Motion - For the 3 kg mass (which will accelerate upwards), the equation of motion can be written as: \[ T - 3g = 3a \quad \text{(Equation 1)} \] - For the 5 kg mass (which will accelerate downwards), the equation of motion can be written as: \[ 5g - T = 5a \quad \text{(Equation 2)} \] ### Step 3: Substitute the Value of g Given \( g = 10 \, \text{m/s}^2 \): - Substitute \( g \) into the equations: - Equation 1 becomes: \[ T - 30 = 3a \] - Equation 2 becomes: \[ 50 - T = 5a \] ### Step 4: Solve the Equations Simultaneously - Rearranging Equation 1 gives: \[ T = 3a + 30 \quad \text{(Equation 3)} \] - Rearranging Equation 2 gives: \[ T = 50 - 5a \quad \text{(Equation 4)} \] ### Step 5: Set Equations 3 and 4 Equal to Each Other Since both equations equal \( T \): \[ 3a + 30 = 50 - 5a \] ### Step 6: Solve for Acceleration (a) - Rearranging gives: \[ 3a + 5a = 50 - 30 \] \[ 8a = 20 \] \[ a = \frac{20}{8} = 2.5 \, \text{m/s}^2 \] ### Step 7: Calculate the Tension (T) - Substitute \( a \) back into Equation 3: \[ T = 3(2.5) + 30 = 7.5 + 30 = 37.5 \, \text{N} \] ### Step 8: Calculate the Thrust on the Pulley - The thrust on the pulley (which is the total force acting on it due to both tensions) is given by: \[ \text{Thrust} = 2T = 2 \times 37.5 = 75 \, \text{N} \] ### Final Answer The thrust on the pulley is \( 75 \, \text{N} \). ---
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