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A rigid homogeneous uniform block of mass 1 kg, height ℎ = 0.4 m and width b = 0.3 m is pinned at one corner and placed upright in a uniform gravitational field (g = 9.81 m/s2), supported by a roller in the configuration shown in the figure. A short duration (impulsive) force F, producing an impulse IF , is applied at a height of d = 0.3 m from the bottom as shown. Assume all joints to be frictionless. The minimum value of IF required to topple the block is
- a)0.953 Ns
- b)1.403 Ns
- c)0.814 Ns
- d)1.172 Ns
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A rigid homogeneous uniform block of mass 1 kg, height = 0.4 m and wi...
Where, G = centre of gravity point
For ΔAOG:
r = 0.25 m
Moment of intertial about point O :
Applying parallel axis theorem,
Where, IG = moment of inertia about its centre,
m = mass of block
We know, moment of inertia of rectangular block,
By putting in equation (i),
I0 = 0.0208+ 1(0.25)2
I0 = 0.0833 kgm2
Now, net moment (∑M0) = I0α
Integrating the equation by taking limit from initial position 1 (not topple) to final position 2 (toppled).
Here,
representing impulse force, ( IF) .
Since, the impulsive force is acting for short duration, therefore neglecting, dt = 0
Now,
(ω1 is at initial position during not topple will be zero)
Then, at position 2 the block will come in angular motion with w2 but after shifting of centroid point i.e. G along the axis of point 'O' let say position 3, at position 3, ω3 will become zero because at this point angular rotation will be due to shifting of centroid of block and eccentric distance will produce torque that will be the actual reason of rotation only.
OG = r = 0.25 m, OK = 0.2 m
Δh = OG - OK
Δh = 0.25 - 0.2
Δh= 0.05 m
Balancing energy conservation for position (2) and position (3) :
By putting in equation (ii),
Impulse, IF = 0.953 N-s
Hence, the correct option is (A).
(ω1 is at initial position during not topple will be zero)
Then, at position 2 the block will come in angular motion with w2 but after shifting of centroid point i.e. G along the axis of point 'O' let say position 3, at position 3, ω3 will become zero because at this point angular rotation will be due to shifting of centroid of block and eccentric distance will produce torque that will be the actual reason of rotation only.
OG = r = 0.25 m, OK = 0.2 m
Δh = OG - OK
Δh = 0.25 - 0.2
Δh= 0.05 m
Balancing energy conservation for position (2) and position (3) :
By putting in equation (ii),
Impulse, IF = 0.953 N-s
Hence, the correct option is (A).
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A rigid homogeneous uniform block of mass 1 kg, height = 0.4 m and width b = 0.3 m is pinned at one corner and placed upright in a uniform gravitational field (g = 9.81 m/s2), supported by a roller in the configuration shown in the figure. A short duration (impulsive) force F, producing an impulse IF , is applied at a height of d = 0.3 m from the bottom as shown. Assume all joints to be frictionless. The minimum value of IF required to topple the block isa)0.953 Nsb)1.403 Nsc)0.814 Nsd)1.172 NsCorrect answer is option 'A'. Can you explain this answer?
Question Description
A rigid homogeneous uniform block of mass 1 kg, height = 0.4 m and width b = 0.3 m is pinned at one corner and placed upright in a uniform gravitational field (g = 9.81 m/s2), supported by a roller in the configuration shown in the figure. A short duration (impulsive) force F, producing an impulse IF , is applied at a height of d = 0.3 m from the bottom as shown. Assume all joints to be frictionless. The minimum value of IF required to topple the block isa)0.953 Nsb)1.403 Nsc)0.814 Nsd)1.172 NsCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A rigid homogeneous uniform block of mass 1 kg, height = 0.4 m and width b = 0.3 m is pinned at one corner and placed upright in a uniform gravitational field (g = 9.81 m/s2), supported by a roller in the configuration shown in the figure. A short duration (impulsive) force F, producing an impulse IF , is applied at a height of d = 0.3 m from the bottom as shown. Assume all joints to be frictionless. The minimum value of IF required to topple the block isa)0.953 Nsb)1.403 Nsc)0.814 Nsd)1.172 NsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rigid homogeneous uniform block of mass 1 kg, height = 0.4 m and width b = 0.3 m is pinned at one corner and placed upright in a uniform gravitational field (g = 9.81 m/s2), supported by a roller in the configuration shown in the figure. A short duration (impulsive) force F, producing an impulse IF , is applied at a height of d = 0.3 m from the bottom as shown. Assume all joints to be frictionless. The minimum value of IF required to topple the block isa)0.953 Nsb)1.403 Nsc)0.814 Nsd)1.172 NsCorrect answer is option 'A'. Can you explain this answer?.
A rigid homogeneous uniform block of mass 1 kg, height = 0.4 m and width b = 0.3 m is pinned at one corner and placed upright in a uniform gravitational field (g = 9.81 m/s2), supported by a roller in the configuration shown in the figure. A short duration (impulsive) force F, producing an impulse IF , is applied at a height of d = 0.3 m from the bottom as shown. Assume all joints to be frictionless. The minimum value of IF required to topple the block isa)0.953 Nsb)1.403 Nsc)0.814 Nsd)1.172 NsCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A rigid homogeneous uniform block of mass 1 kg, height = 0.4 m and width b = 0.3 m is pinned at one corner and placed upright in a uniform gravitational field (g = 9.81 m/s2), supported by a roller in the configuration shown in the figure. A short duration (impulsive) force F, producing an impulse IF , is applied at a height of d = 0.3 m from the bottom as shown. Assume all joints to be frictionless. The minimum value of IF required to topple the block isa)0.953 Nsb)1.403 Nsc)0.814 Nsd)1.172 NsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rigid homogeneous uniform block of mass 1 kg, height = 0.4 m and width b = 0.3 m is pinned at one corner and placed upright in a uniform gravitational field (g = 9.81 m/s2), supported by a roller in the configuration shown in the figure. A short duration (impulsive) force F, producing an impulse IF , is applied at a height of d = 0.3 m from the bottom as shown. Assume all joints to be frictionless. The minimum value of IF required to topple the block isa)0.953 Nsb)1.403 Nsc)0.814 Nsd)1.172 NsCorrect answer is option 'A'. Can you explain this answer?.
Solutions for A rigid homogeneous uniform block of mass 1 kg, height = 0.4 m and width b = 0.3 m is pinned at one corner and placed upright in a uniform gravitational field (g = 9.81 m/s2), supported by a roller in the configuration shown in the figure. A short duration (impulsive) force F, producing an impulse IF , is applied at a height of d = 0.3 m from the bottom as shown. Assume all joints to be frictionless. The minimum value of IF required to topple the block isa)0.953 Nsb)1.403 Nsc)0.814 Nsd)1.172 NsCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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