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A hemispherical bowl of radius R = 0.1m is rotating about its own axis (which is vertical) with an angular velocity ω. A particle of mass 10–2 kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl. It is desired to measure 'g' using this set up, by measuring h accurately. Assuming that R and ω are known precisely and that the least-count in the measurement of h is 10–4 m, the numerical value of minimum possible error Δg in the measured value of g is given by α x 10–2 m/s2. Fill the value of α in OMR sheet.
Correct answer is '1'. Can you explain this answer?
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A hemispherical bowl of radius R = 0.1m is rotating about its own axis...
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A hemispherical bowl of radius R = 0.1m is rotating about its own axis...
1. **Calculation of Error in Measured Value of g**:
- The net gravitational force acting on the particle on the inner surface of the bowl can be given as:
F_net = m*g - m*(Rω)^2
- At the maximum height h, the particle will experience maximum acceleration towards the center of the bowl:
a_max = g + Rω^2
- The height h can be calculated using the equation:
h = R - R*cos(θ)
- Differentiating with respect to time t:
dh/dt = Rωsin(θ)*dθ/dt
- Since the particle is rotating with the same angular velocity ω, dθ/dt = ω, giving:
dh/dt = Rωsin(θ)
2. **Error Analysis**:
- The error in measuring h, Δh, is given as:
Δh = 10^-4 m
- The maximum possible error in measurement of h, Δh_max, can be calculated by considering the maximum value of sin(θ):
Δh_max = Rω
- The error in measurement of g, Δg, can be calculated using the formula:
Δg = Δh_max * ω^2
3. **Final Calculation**:
- Substituting the known values R = 0.1m and ω into the above formula, we get:
Δg = 0.1*1^2 = 0.1 m/s^2 = 1 x 10^-2 m/s^2
Therefore, the numerical value of minimum possible error Δg in the measured value of g is 1 x 10^-2 m/s^2.
- The net gravitational force acting on the particle on the inner surface of the bowl can be given as:
F_net = m*g - m*(Rω)^2
- At the maximum height h, the particle will experience maximum acceleration towards the center of the bowl:
a_max = g + Rω^2
- The height h can be calculated using the equation:
h = R - R*cos(θ)
- Differentiating with respect to time t:
dh/dt = Rωsin(θ)*dθ/dt
- Since the particle is rotating with the same angular velocity ω, dθ/dt = ω, giving:
dh/dt = Rωsin(θ)
2. **Error Analysis**:
- The error in measuring h, Δh, is given as:
Δh = 10^-4 m
- The maximum possible error in measurement of h, Δh_max, can be calculated by considering the maximum value of sin(θ):
Δh_max = Rω
- The error in measurement of g, Δg, can be calculated using the formula:
Δg = Δh_max * ω^2
3. **Final Calculation**:
- Substituting the known values R = 0.1m and ω into the above formula, we get:
Δg = 0.1*1^2 = 0.1 m/s^2 = 1 x 10^-2 m/s^2
Therefore, the numerical value of minimum possible error Δg in the measured value of g is 1 x 10^-2 m/s^2.
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A hemispherical bowl of radius R = 0.1m is rotating about its own axis (which is vertical) with an angular velocity ω. A particle of mass 10–2kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl. It is desired to measure g using this set up, by measuring h accurately. Assuming that R and ω are known precisely and that the least-count in the measurement of h is 10–4m, the numerical value of minimum possible error Δg in the measured value of g is given byα x10–2m/s2. Fill the value of α in OMR sheet.Correct answer is '1'. Can you explain this answer?
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A hemispherical bowl of radius R = 0.1m is rotating about its own axis (which is vertical) with an angular velocity ω. A particle of mass 10–2kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl. It is desired to measure g using this set up, by measuring h accurately. Assuming that R and ω are known precisely and that the least-count in the measurement of h is 10–4m, the numerical value of minimum possible error Δg in the measured value of g is given byα x10–2m/s2. Fill the value of α in OMR sheet.Correct answer is '1'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A hemispherical bowl of radius R = 0.1m is rotating about its own axis (which is vertical) with an angular velocity ω. A particle of mass 10–2kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl. It is desired to measure g using this set up, by measuring h accurately. Assuming that R and ω are known precisely and that the least-count in the measurement of h is 10–4m, the numerical value of minimum possible error Δg in the measured value of g is given byα x10–2m/s2. Fill the value of α in OMR sheet.Correct answer is '1'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hemispherical bowl of radius R = 0.1m is rotating about its own axis (which is vertical) with an angular velocity ω. A particle of mass 10–2kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl. It is desired to measure g using this set up, by measuring h accurately. Assuming that R and ω are known precisely and that the least-count in the measurement of h is 10–4m, the numerical value of minimum possible error Δg in the measured value of g is given byα x10–2m/s2. Fill the value of α in OMR sheet.Correct answer is '1'. Can you explain this answer?.
A hemispherical bowl of radius R = 0.1m is rotating about its own axis (which is vertical) with an angular velocity ω. A particle of mass 10–2kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl. It is desired to measure g using this set up, by measuring h accurately. Assuming that R and ω are known precisely and that the least-count in the measurement of h is 10–4m, the numerical value of minimum possible error Δg in the measured value of g is given byα x10–2m/s2. Fill the value of α in OMR sheet.Correct answer is '1'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A hemispherical bowl of radius R = 0.1m is rotating about its own axis (which is vertical) with an angular velocity ω. A particle of mass 10–2kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl. It is desired to measure g using this set up, by measuring h accurately. Assuming that R and ω are known precisely and that the least-count in the measurement of h is 10–4m, the numerical value of minimum possible error Δg in the measured value of g is given byα x10–2m/s2. Fill the value of α in OMR sheet.Correct answer is '1'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hemispherical bowl of radius R = 0.1m is rotating about its own axis (which is vertical) with an angular velocity ω. A particle of mass 10–2kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl. It is desired to measure g using this set up, by measuring h accurately. Assuming that R and ω are known precisely and that the least-count in the measurement of h is 10–4m, the numerical value of minimum possible error Δg in the measured value of g is given byα x10–2m/s2. Fill the value of α in OMR sheet.Correct answer is '1'. Can you explain this answer?.
Solutions for A hemispherical bowl of radius R = 0.1m is rotating about its own axis (which is vertical) with an angular velocity ω. A particle of mass 10–2kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl. It is desired to measure g using this set up, by measuring h accurately. Assuming that R and ω are known precisely and that the least-count in the measurement of h is 10–4m, the numerical value of minimum possible error Δg in the measured value of g is given byα x10–2m/s2. Fill the value of α in OMR sheet.Correct answer is '1'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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A hemispherical bowl of radius R = 0.1m is rotating about its own axis (which is vertical) with an angular velocity ω. A particle of mass 10–2kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl. It is desired to measure g using this set up, by measuring h accurately. Assuming that R and ω are known precisely and that the least-count in the measurement of h is 10–4m, the numerical value of minimum possible error Δg in the measured value of g is given byα x10–2m/s2. Fill the value of α in OMR sheet.Correct answer is '1'. Can you explain this answer?, a detailed solution for A hemispherical bowl of radius R = 0.1m is rotating about its own axis (which is vertical) with an angular velocity ω. A particle of mass 10–2kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl. It is desired to measure g using this set up, by measuring h accurately. Assuming that R and ω are known precisely and that the least-count in the measurement of h is 10–4m, the numerical value of minimum possible error Δg in the measured value of g is given byα x10–2m/s2. Fill the value of α in OMR sheet.Correct answer is '1'. Can you explain this answer? has been provided alongside types of A hemispherical bowl of radius R = 0.1m is rotating about its own axis (which is vertical) with an angular velocity ω. A particle of mass 10–2kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl. It is desired to measure g using this set up, by measuring h accurately. Assuming that R and ω are known precisely and that the least-count in the measurement of h is 10–4m, the numerical value of minimum possible error Δg in the measured value of g is given byα x10–2m/s2. Fill the value of α in OMR sheet.Correct answer is '1'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A hemispherical bowl of radius R = 0.1m is rotating about its own axis (which is vertical) with an angular velocity ω. A particle of mass 10–2kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl. It is desired to measure g using this set up, by measuring h accurately. Assuming that R and ω are known precisely and that the least-count in the measurement of h is 10–4m, the numerical value of minimum possible error Δg in the measured value of g is given byα x10–2m/s2. Fill the value of α in OMR sheet.Correct answer is '1'. Can you explain this answer? tests, examples and also practice JEE tests.
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