Question

Two blocks of masses 5 kg and 2 kg (see fig.) are initially at rest on the floor.



They are connected by a light string, passing over a light frictionless

pulley. An upward force F is applied on the pulley and maintained

constant. Calculate the acceleration a1

and a2

of the 5 kg and 2

kg masses, respectively, when F is 110 N (g = 10 msñ2

).

Answer 1

the block will be lifted only when the tension of stirng exceeds the gravitational pull on them.

gravitational force = mg + Mg
= 2kg × 10m/s² + 5kg × 10m/s² = 70 N

Let's check , F - 2T = 0 [ see free body daigram as shown in figure ]
given, F = 110N
110 - 2T = 0 => T = 55 N

tension is greater than gravitational pull { e.g., 55N >50N and 55N > 20N}

so, use Newton's law of motion separately for both blocks

acceleration of block of mass 2kg is a ,
T - mg = ma
55 - 2 × 10 = 2 × a
55 - 20 = 2a => a = 17.5 m/s²

acceleration of block of mass 5kg is a',
T - Mg = Ma'
55 - 5 × 10 = 5a
55 - 50 = 5a => a = 1 m/s²

Answer 2

Explanation:

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