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A hydraulic press has a ram of 20 cm diameter and a plunger of 5 cm diameter. The force required at the plunger to lift a weight of 16 x 104 N shall be
- a)256 x 104 N
- b)64 x 104 N
- c)4 x 104 N
- d)1x 104 N
Correct answer is option 'D'. Can you explain this answer?
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A hydraulic press has a ram of 20 cm diameter and a plunger of 5 cm d...
F2 = 1x 104 N
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To find the force required at the plunger to lift a weight of 16 x 10^4 N, we can use Pascal's law, which states that the pressure in a fluid is transmitted equally in all directions.
Given:
Diameter of the ram = 20 cm
Radius of the ram = 10 cm
Area of the ram = πr^2 = π(10^2) = 100π cm^2
Diameter of the plunger = 5 cm
Radius of the plunger = 2.5 cm
Area of the plunger = πr^2 = π(2.5^2) = 6.25π cm^2
Weight to be lifted = 16 x 10^4 N
Using Pascal's law, we can say that the pressure at the ram is equal to the pressure at the plunger. Therefore, the force at the ram is equal to the force at the plunger.
Let F_r be the force at the ram, and F_p be the force at the plunger.
Given that the weight to be lifted is 16 x 10^4 N, which is equal to the force at the plunger (F_p).
Using the formula for pressure (P = F/A), we can calculate the pressure at the ram (P_r) and the pressure at the plunger (P_p).
Pressure at the ram:
P_r = F_r / A_r
P_r = F_r / (100π)
Pressure at the plunger:
P_p = F_p / A_p
P_p = F_p / (6.25π)
Since the pressure at the ram (P_r) is equal to the pressure at the plunger (P_p), we can equate the two equations:
F_r / (100π) = F_p / (6.25π)
Canceling out the common factor of π, we get:
F_r / 100 = F_p / 6.25
Cross multiplying, we get:
F_r = (F_p * 100) / 6.25
Substituting the value of F_p (16 x 10^4 N), we get:
F_r = (16 x 10^4 * 100) / 6.25
F_r = 256 x 10^4 / 6.25
F_r = 40 x 10^4 N
Therefore, the force required at the plunger to lift a weight of 16 x 10^4 N is 40 x 10^4 N, which is equivalent to 4 x 10^4 N. Hence, the correct answer is option D.
Given:
Diameter of the ram = 20 cm
Radius of the ram = 10 cm
Area of the ram = πr^2 = π(10^2) = 100π cm^2
Diameter of the plunger = 5 cm
Radius of the plunger = 2.5 cm
Area of the plunger = πr^2 = π(2.5^2) = 6.25π cm^2
Weight to be lifted = 16 x 10^4 N
Using Pascal's law, we can say that the pressure at the ram is equal to the pressure at the plunger. Therefore, the force at the ram is equal to the force at the plunger.
Let F_r be the force at the ram, and F_p be the force at the plunger.
Given that the weight to be lifted is 16 x 10^4 N, which is equal to the force at the plunger (F_p).
Using the formula for pressure (P = F/A), we can calculate the pressure at the ram (P_r) and the pressure at the plunger (P_p).
Pressure at the ram:
P_r = F_r / A_r
P_r = F_r / (100π)
Pressure at the plunger:
P_p = F_p / A_p
P_p = F_p / (6.25π)
Since the pressure at the ram (P_r) is equal to the pressure at the plunger (P_p), we can equate the two equations:
F_r / (100π) = F_p / (6.25π)
Canceling out the common factor of π, we get:
F_r / 100 = F_p / 6.25
Cross multiplying, we get:
F_r = (F_p * 100) / 6.25
Substituting the value of F_p (16 x 10^4 N), we get:
F_r = (16 x 10^4 * 100) / 6.25
F_r = 256 x 10^4 / 6.25
F_r = 40 x 10^4 N
Therefore, the force required at the plunger to lift a weight of 16 x 10^4 N is 40 x 10^4 N, which is equivalent to 4 x 10^4 N. Hence, the correct answer is option D.
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A hydraulic press has a ram of 20 cm diameter and a plunger of 5 cm diameter. The force required at the plunger to lift a weight of 16 x 104 N shall bea)256 x 104 Nb)64 x 104 Nc)4 x 104 Nd)1x 104 NCorrect answer is option 'D'. Can you explain this answer?
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A hydraulic press has a ram of 20 cm diameter and a plunger of 5 cm diameter. The force required at the plunger to lift a weight of 16 x 104 N shall bea)256 x 104 Nb)64 x 104 Nc)4 x 104 Nd)1x 104 NCorrect answer is option 'D'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about A hydraulic press has a ram of 20 cm diameter and a plunger of 5 cm diameter. The force required at the plunger to lift a weight of 16 x 104 N shall bea)256 x 104 Nb)64 x 104 Nc)4 x 104 Nd)1x 104 NCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hydraulic press has a ram of 20 cm diameter and a plunger of 5 cm diameter. The force required at the plunger to lift a weight of 16 x 104 N shall bea)256 x 104 Nb)64 x 104 Nc)4 x 104 Nd)1x 104 NCorrect answer is option 'D'. Can you explain this answer?.
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