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Two masses M1 and M2 are connected by light string which passes over the top of smooth plane inclined at 30 degree to the horizontal so that one mass rests on the plane and the other hangs vertically .it is found that M1 hanging vertically can draws M2 up the full length of the plane in half time in which M2 hanging vertically draws M1 up .find the ratio of M1:M2 .assume pulley to be smooth?
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Two masses M1 and M2 are connected by light string which passes over t...
Given:
- Two masses M1 and M2 are connected by a light string.
- The string passes over a smooth plane inclined at 30 degrees to the horizontal.
- One mass rests on the plane, while the other hangs vertically.
- It is observed that M1 hanging vertically can draw M2 up the full length of the plane in half the time it takes for M2 hanging vertically to draw M1 up.
To Find:
The ratio of M1 to M2.
Explanation:
Let's assume M1 is the mass hanging vertically and M2 is the mass resting on the inclined plane.
Step 1: Drawing Free Body Diagrams
We need to draw the free body diagrams for both masses to analyze the forces acting on them.
For M1:
- Tension in the string T1 acts upward.
- The weight of M1 (M1 * g) acts downward.
For M2:
- Tension in the string T2 acts downward.
- The component of M2's weight parallel to the inclined plane (M2 * g * sin(30°)) acts downward.
- The component of M2's weight perpendicular to the inclined plane (M2 * g * cos(30°)) acts perpendicular to the inclined plane.
Step 2: Analyzing Forces
For M1:
- The net force acting upward is T1.
- The net force acting downward is M1 * g.
For M2:
- The net force acting upward is the component of M2's weight parallel to the inclined plane (M2 * g * sin(30°)).
- The net force acting downward is T2 + the component of M2's weight perpendicular to the inclined plane (M2 * g * cos(30°)).
Step 3: Applying Newton's Second Law
For M1:
- The acceleration of M1 is given by T1 / M1.
- According to the given information, M1 can draw M2 up the full length of the plane in half the time it takes for M2 to draw M1 up. This implies that the acceleration of M1 is twice the acceleration of M2.
For M2:
- The acceleration of M2 is given by (M2 * g * sin(30°) - T2 - M2 * g * cos(30°)) / M2.
Step 4: Equating Accelerations and Solving
Since the acceleration of M1 is twice the acceleration of M2, we can equate the two expressions for acceleration and solve for the ratio of M1 to M2.
T1 / M1 = 2 * [(M2 * g * sin(30°) - T2 - M2 * g * cos(30°)) / M2]
Simplifying the equation:
T1 = 2 * (M2 * g * sin(30°) - T2 - M2 * g * cos(30°)) * (M1 / M2)
Step 5: Solving for Tensions
Since the pulley is assumed to be smooth, the tensions in the string T1 and T2 are equal.
T1 = T2
Substituting this into the equation above:
T2 = 2 * (M2 * g * sin(
- Two masses M1 and M2 are connected by a light string.
- The string passes over a smooth plane inclined at 30 degrees to the horizontal.
- One mass rests on the plane, while the other hangs vertically.
- It is observed that M1 hanging vertically can draw M2 up the full length of the plane in half the time it takes for M2 hanging vertically to draw M1 up.
To Find:
The ratio of M1 to M2.
Explanation:
Let's assume M1 is the mass hanging vertically and M2 is the mass resting on the inclined plane.
Step 1: Drawing Free Body Diagrams
We need to draw the free body diagrams for both masses to analyze the forces acting on them.
For M1:
- Tension in the string T1 acts upward.
- The weight of M1 (M1 * g) acts downward.
For M2:
- Tension in the string T2 acts downward.
- The component of M2's weight parallel to the inclined plane (M2 * g * sin(30°)) acts downward.
- The component of M2's weight perpendicular to the inclined plane (M2 * g * cos(30°)) acts perpendicular to the inclined plane.
Step 2: Analyzing Forces
For M1:
- The net force acting upward is T1.
- The net force acting downward is M1 * g.
For M2:
- The net force acting upward is the component of M2's weight parallel to the inclined plane (M2 * g * sin(30°)).
- The net force acting downward is T2 + the component of M2's weight perpendicular to the inclined plane (M2 * g * cos(30°)).
Step 3: Applying Newton's Second Law
For M1:
- The acceleration of M1 is given by T1 / M1.
- According to the given information, M1 can draw M2 up the full length of the plane in half the time it takes for M2 to draw M1 up. This implies that the acceleration of M1 is twice the acceleration of M2.
For M2:
- The acceleration of M2 is given by (M2 * g * sin(30°) - T2 - M2 * g * cos(30°)) / M2.
Step 4: Equating Accelerations and Solving
Since the acceleration of M1 is twice the acceleration of M2, we can equate the two expressions for acceleration and solve for the ratio of M1 to M2.
T1 / M1 = 2 * [(M2 * g * sin(30°) - T2 - M2 * g * cos(30°)) / M2]
Simplifying the equation:
T1 = 2 * (M2 * g * sin(30°) - T2 - M2 * g * cos(30°)) * (M1 / M2)
Step 5: Solving for Tensions
Since the pulley is assumed to be smooth, the tensions in the string T1 and T2 are equal.
T1 = T2
Substituting this into the equation above:
T2 = 2 * (M2 * g * sin(
Community Answer
Two masses M1 and M2 are connected by light string which passes over t...
Use direct formula
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Two masses M1 and M2 are connected by light string which passes over the top of smooth plane inclined at 30 degree to the horizontal so that one mass rests on the plane and the other hangs vertically .it is found that M1 hanging vertically can draws M2 up the full length of the plane in half time in which M2 hanging vertically draws M1 up .find the ratio of M1:M2 .assume pulley to be smooth?
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Two masses M1 and M2 are connected by light string which passes over the top of smooth plane inclined at 30 degree to the horizontal so that one mass rests on the plane and the other hangs vertically .it is found that M1 hanging vertically can draws M2 up the full length of the plane in half time in which M2 hanging vertically draws M1 up .find the ratio of M1:M2 .assume pulley to be smooth? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two masses M1 and M2 are connected by light string which passes over the top of smooth plane inclined at 30 degree to the horizontal so that one mass rests on the plane and the other hangs vertically .it is found that M1 hanging vertically can draws M2 up the full length of the plane in half time in which M2 hanging vertically draws M1 up .find the ratio of M1:M2 .assume pulley to be smooth? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two masses M1 and M2 are connected by light string which passes over the top of smooth plane inclined at 30 degree to the horizontal so that one mass rests on the plane and the other hangs vertically .it is found that M1 hanging vertically can draws M2 up the full length of the plane in half time in which M2 hanging vertically draws M1 up .find the ratio of M1:M2 .assume pulley to be smooth?.
Two masses M1 and M2 are connected by light string which passes over the top of smooth plane inclined at 30 degree to the horizontal so that one mass rests on the plane and the other hangs vertically .it is found that M1 hanging vertically can draws M2 up the full length of the plane in half time in which M2 hanging vertically draws M1 up .find the ratio of M1:M2 .assume pulley to be smooth? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two masses M1 and M2 are connected by light string which passes over the top of smooth plane inclined at 30 degree to the horizontal so that one mass rests on the plane and the other hangs vertically .it is found that M1 hanging vertically can draws M2 up the full length of the plane in half time in which M2 hanging vertically draws M1 up .find the ratio of M1:M2 .assume pulley to be smooth? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two masses M1 and M2 are connected by light string which passes over the top of smooth plane inclined at 30 degree to the horizontal so that one mass rests on the plane and the other hangs vertically .it is found that M1 hanging vertically can draws M2 up the full length of the plane in half time in which M2 hanging vertically draws M1 up .find the ratio of M1:M2 .assume pulley to be smooth?.
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Two masses M1 and M2 are connected by light string which passes over the top of smooth plane inclined at 30 degree to the horizontal so that one mass rests on the plane and the other hangs vertically .it is found that M1 hanging vertically can draws M2 up the full length of the plane in half time in which M2 hanging vertically draws M1 up .find the ratio of M1:M2 .assume pulley to be smooth?, a detailed solution for Two masses M1 and M2 are connected by light string which passes over the top of smooth plane inclined at 30 degree to the horizontal so that one mass rests on the plane and the other hangs vertically .it is found that M1 hanging vertically can draws M2 up the full length of the plane in half time in which M2 hanging vertically draws M1 up .find the ratio of M1:M2 .assume pulley to be smooth? has been provided alongside types of Two masses M1 and M2 are connected by light string which passes over the top of smooth plane inclined at 30 degree to the horizontal so that one mass rests on the plane and the other hangs vertically .it is found that M1 hanging vertically can draws M2 up the full length of the plane in half time in which M2 hanging vertically draws M1 up .find the ratio of M1:M2 .assume pulley to be smooth? theory, EduRev gives you an
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