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A mass of M kg is suspended by weightless string. The horizontal force that is required to displace it until the string makes an angle of 45 with the initial vertical direction is??
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A mass of M kg is suspended by weightless string. The horizontal force...
Understanding the Problem
When a mass M kg is suspended by a weightless string and displaced to make an angle of 45 degrees with the vertical, we can analyze the forces acting on the mass to determine the horizontal force required.
Forces Acting on the Mass
- Weight (W): The force due to gravity acting downwards, calculated as W = M * g, where g is the acceleration due to gravity (approximately 9.81 m/s²).
- Tension (T): The force exerted by the string, acting along the string at an angle of 45 degrees from the vertical.
- Horizontal Force (F): The external horizontal force applied to displace the mass.
Force Balance at 45 Degrees
At the angle of 45 degrees, the tension in the string can be resolved into two components:
- Vertical Component (T_y): T_y = T * cos(45°) = T / √2
- Horizontal Component (T_x): T_x = T * sin(45°) = T / √2
Since the mass is in equilibrium vertically:
- T_y = Weight (W)
Thus, T / √2 = M * g, leading to T = M * g * √2.
Calculating the Horizontal Force
In horizontal equilibrium:
- F = T_x = T / √2
Substituting the expression for T, we have:
F = (M * g * √2) / √2 = M * g.
Conclusion
The horizontal force required to displace the mass until the string makes a 45-degree angle with the vertical is:
- F = M * g.
This means that the applied horizontal force equals the weight of the mass.
When a mass M kg is suspended by a weightless string and displaced to make an angle of 45 degrees with the vertical, we can analyze the forces acting on the mass to determine the horizontal force required.
Forces Acting on the Mass
- Weight (W): The force due to gravity acting downwards, calculated as W = M * g, where g is the acceleration due to gravity (approximately 9.81 m/s²).
- Tension (T): The force exerted by the string, acting along the string at an angle of 45 degrees from the vertical.
- Horizontal Force (F): The external horizontal force applied to displace the mass.
Force Balance at 45 Degrees
At the angle of 45 degrees, the tension in the string can be resolved into two components:
- Vertical Component (T_y): T_y = T * cos(45°) = T / √2
- Horizontal Component (T_x): T_x = T * sin(45°) = T / √2
Since the mass is in equilibrium vertically:
- T_y = Weight (W)
Thus, T / √2 = M * g, leading to T = M * g * √2.
Calculating the Horizontal Force
In horizontal equilibrium:
- F = T_x = T / √2
Substituting the expression for T, we have:
F = (M * g * √2) / √2 = M * g.
Conclusion
The horizontal force required to displace the mass until the string makes a 45-degree angle with the vertical is:
- F = M * g.
This means that the applied horizontal force equals the weight of the mass.
Community Answer
A mass of M kg is suspended by weightless string. The horizontal force...
is it Mg / √2
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A mass of M kg is suspended by weightless string. The horizontal force that is required to displace it until the string makes an angle of 45 with the initial vertical direction is??
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A mass of M kg is suspended by weightless string. The horizontal force that is required to displace it until the string makes an angle of 45 with the initial vertical direction is?? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A mass of M kg is suspended by weightless string. The horizontal force that is required to displace it until the string makes an angle of 45 with the initial vertical direction is?? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mass of M kg is suspended by weightless string. The horizontal force that is required to displace it until the string makes an angle of 45 with the initial vertical direction is??.
A mass of M kg is suspended by weightless string. The horizontal force that is required to displace it until the string makes an angle of 45 with the initial vertical direction is?? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A mass of M kg is suspended by weightless string. The horizontal force that is required to displace it until the string makes an angle of 45 with the initial vertical direction is?? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mass of M kg is suspended by weightless string. The horizontal force that is required to displace it until the string makes an angle of 45 with the initial vertical direction is??.
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