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Block on a table pulled by a hanging mass over a pulley: acceleration or tension

This type of question, asked 3 times: 28 Jun 2022, 29 Jun 2022, 1 Feb 2024. All 3 questions below, oldest first.

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  1. Question 1

    28 Jun 2022

    27
    A hanging mass MM is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2Mg2Mg force. In this situation, tension in the string is x5\frac{x}{5} MgMg for x=____x = \_\_\_\_. Neglect mass of the string and friction of the block (bigger mass) with ice slab. (Given g=g = acceleration due to gravity)

  2. Question 2

    29 Jun 2022

    105
    A block of mass 40 kg40\text{ }kg slides over a surface, when a mass of 4 kg4\text{ }kg is suspended through an inextensible massless string passing over frictionless pulley as shown below. The coefficient of kinetic friction between the surface and block is 0.02 . The acceleration of block is. (Given g=10 ms−2g = 10{\text{ }ms}^{- 2}.)

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  3. Question 3

    1 Feb 2024

    18
    Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is 0.04, the acceleration of the system in ms−2ms^{- 2} is: (Consider that the string is massless and unstretchable and the pulley is also massless and frictionless):

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