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Two smooth sphere each of radius 5 cm and weight w rest one on the other inside a fixed smooth cylinder of radius 8 cm . the reactions between the sphere and the vertical side of the cylinder are (a) w/4 and 3w/4 (b) w/4 and w/4 (c) 3w/4 and 3w/4 (d) w and w?
Verified Answer
Two smooth sphere each of radius 5 cm and weight w rest one on the oth...
First get the lengths of various sides. Then the angle of the line joining the two centers of spheres.
F1, F2, F3 and F4 are contact forces of actions and reactions.
W = mg given.
Tan Ф = 4/3. SinФ = 4/5. CosФ = 3/5.
Since the system is in static equilibrium, we balance the horizontal and vertical forces.
F1 = F3 * CosФ = 0.60 F3
W = m g = F3 SinФ = 0.80 F3
=> F3 = 1.25 W. => F1 = 0.750 W.
W + F3 SinФ = F4
F4 = W + W = 2 W
F2 = F3 CosФ = F1 = 0.750 W
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Most Upvoted Answer
Two smooth sphere each of radius 5 cm and weight w rest one on the oth...
Analysis:
To solve this problem, we need to consider the forces acting on each sphere and the equilibrium conditions. Let's break down the problem into smaller steps.
Step 1: Identifying the forces:
The forces acting on each sphere are:
1. Weight (W): The force due to gravity acting vertically downwards on each sphere.
2. Normal reaction (N1 and N2): The reactions between the spheres and the vertical side of the cylinder.
Step 2: Equilibrium of forces:
Since the spheres are at rest, the net force acting on each sphere in both the horizontal and vertical directions must be zero. This implies that the sum of all the forces acting on each sphere must be zero.
Step 3: Horizontal equilibrium:
Since the spheres are in contact with each other, the horizontal forces cancel out. Therefore, the horizontal components of the forces can be ignored.
Step 4: Vertical equilibrium:
Considering the vertical forces, we can write the following equation for each sphere:
For the top sphere:
N1 - W = 0 ...(Equation 1)
For the bottom sphere:
N2 - N1 - W = 0 ...(Equation 2)
Step 5: Solving the equations:
Substituting the weight of each sphere into the equations, we get:
For the top sphere:
N1 - W = 0
N1 - W = 0
N1 - 2W = 0 ...(Equation 3)
For the bottom sphere:
N2 - N1 - W = 0 ...(Equation 4)
Step 6: Solving for the reactions:
Now, substituting the values of the weights of the spheres:
For the top sphere:
N1 - 2W = 0
N1 - 2W = 0
N1 - 2(5) = 0
N1 - 10 = 0
N1 = 10 ...(Equation 5)
For the bottom sphere:
N2 - N1 - W = 0
N2 - 10 - 5 = 0
N2 - 15 = 0
N2 = 15 ...(Equation 6)
Step 7: Final result:
From equations 5 and 6, we can conclude that the reactions between the spheres and the vertical side of the cylinder are N1 = 10 and N2 = 15.
Answer:
The correct option is (c) 3w/4 and 3w/4.
To solve this problem, we need to consider the forces acting on each sphere and the equilibrium conditions. Let's break down the problem into smaller steps.
Step 1: Identifying the forces:
The forces acting on each sphere are:
1. Weight (W): The force due to gravity acting vertically downwards on each sphere.
2. Normal reaction (N1 and N2): The reactions between the spheres and the vertical side of the cylinder.
Step 2: Equilibrium of forces:
Since the spheres are at rest, the net force acting on each sphere in both the horizontal and vertical directions must be zero. This implies that the sum of all the forces acting on each sphere must be zero.
Step 3: Horizontal equilibrium:
Since the spheres are in contact with each other, the horizontal forces cancel out. Therefore, the horizontal components of the forces can be ignored.
Step 4: Vertical equilibrium:
Considering the vertical forces, we can write the following equation for each sphere:
For the top sphere:
N1 - W = 0 ...(Equation 1)
For the bottom sphere:
N2 - N1 - W = 0 ...(Equation 2)
Step 5: Solving the equations:
Substituting the weight of each sphere into the equations, we get:
For the top sphere:
N1 - W = 0
N1 - W = 0
N1 - 2W = 0 ...(Equation 3)
For the bottom sphere:
N2 - N1 - W = 0 ...(Equation 4)
Step 6: Solving for the reactions:
Now, substituting the values of the weights of the spheres:
For the top sphere:
N1 - 2W = 0
N1 - 2W = 0
N1 - 2(5) = 0
N1 - 10 = 0
N1 = 10 ...(Equation 5)
For the bottom sphere:
N2 - N1 - W = 0
N2 - 10 - 5 = 0
N2 - 15 = 0
N2 = 15 ...(Equation 6)
Step 7: Final result:
From equations 5 and 6, we can conclude that the reactions between the spheres and the vertical side of the cylinder are N1 = 10 and N2 = 15.
Answer:
The correct option is (c) 3w/4 and 3w/4.
Community Answer
Two smooth sphere each of radius 5 cm and weight w rest one on the oth...
U can also use....sin frmlaa
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Two smooth sphere each of radius 5 cm and weight w rest one on the other inside a fixed smooth cylinder of radius 8 cm . the reactions between the sphere and the vertical side of the cylinder are (a) w/4 and 3w/4 (b) w/4 and w/4 (c) 3w/4 and 3w/4 (d) w and w?
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Two smooth sphere each of radius 5 cm and weight w rest one on the other inside a fixed smooth cylinder of radius 8 cm . the reactions between the sphere and the vertical side of the cylinder are (a) w/4 and 3w/4 (b) w/4 and w/4 (c) 3w/4 and 3w/4 (d) w and w? 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 smooth sphere each of radius 5 cm and weight w rest one on the other inside a fixed smooth cylinder of radius 8 cm . the reactions between the sphere and the vertical side of the cylinder are (a) w/4 and 3w/4 (b) w/4 and w/4 (c) 3w/4 and 3w/4 (d) w and w? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two smooth sphere each of radius 5 cm and weight w rest one on the other inside a fixed smooth cylinder of radius 8 cm . the reactions between the sphere and the vertical side of the cylinder are (a) w/4 and 3w/4 (b) w/4 and w/4 (c) 3w/4 and 3w/4 (d) w and w?.
Two smooth sphere each of radius 5 cm and weight w rest one on the other inside a fixed smooth cylinder of radius 8 cm . the reactions between the sphere and the vertical side of the cylinder are (a) w/4 and 3w/4 (b) w/4 and w/4 (c) 3w/4 and 3w/4 (d) w and w? 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 smooth sphere each of radius 5 cm and weight w rest one on the other inside a fixed smooth cylinder of radius 8 cm . the reactions between the sphere and the vertical side of the cylinder are (a) w/4 and 3w/4 (b) w/4 and w/4 (c) 3w/4 and 3w/4 (d) w and w? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two smooth sphere each of radius 5 cm and weight w rest one on the other inside a fixed smooth cylinder of radius 8 cm . the reactions between the sphere and the vertical side of the cylinder are (a) w/4 and 3w/4 (b) w/4 and w/4 (c) 3w/4 and 3w/4 (d) w and w?.
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