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A string is wrapped on a wheel of moment of inertia o.20kg m^2and radius10cm and goes through a light pulley to support a block of mass 2kg. Find the acceleration of the block?
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A string is wrapped on a wheel of moment of inertia o.20kg m^2and radi...
Given:
Moment of inertia of the wheel (I) = 0.20 kg m^2
Radius of the wheel (r) = 10 cm = 0.1 m
Mass of the block (m) = 2 kg
To Find:
Acceleration of the block (a)
Formula:
The torque (τ) exerted on the wheel is given by:
τ = Iα
Where:
τ = torque
I = moment of inertia
α = angular acceleration
The torque can also be expressed as:
τ = Fr
Where:
F = force
r = radius of the wheel
The force F is related to the mass and acceleration of the block by Newton's second law:
F = ma
Explanation:
The string wrapped around the wheel causes a torque on the wheel. This torque is transmitted to the block through the light pulley, causing it to accelerate.
Step 1: Calculate the torque exerted on the wheel.
τ = Fr
τ = (ma)r
τ = mar
Step 2: Calculate the angular acceleration of the wheel.
τ = Iα
mar = Iα
α = (mar) / I
Step 3: Convert the linear acceleration of the block to angular acceleration.
The linear acceleration of the block is the same as the angular acceleration of the wheel because they are connected by the string.
So, α = a / r
Step 4: Substitute the value of α in the previous equation.
a / r = (mar) / I
Step 5: Solve for the acceleration of the block (a).
a = (mar^2) / I
Step 6: Substitute the given values into the equation and calculate the acceleration.
a = (2 * 0.1 * 0.1^2) / 0.20
a = 0.01 m/s^2
Answer:
The acceleration of the block is 0.01 m/s^2.
Moment of inertia of the wheel (I) = 0.20 kg m^2
Radius of the wheel (r) = 10 cm = 0.1 m
Mass of the block (m) = 2 kg
To Find:
Acceleration of the block (a)
Formula:
The torque (τ) exerted on the wheel is given by:
τ = Iα
Where:
τ = torque
I = moment of inertia
α = angular acceleration
The torque can also be expressed as:
τ = Fr
Where:
F = force
r = radius of the wheel
The force F is related to the mass and acceleration of the block by Newton's second law:
F = ma
Explanation:
The string wrapped around the wheel causes a torque on the wheel. This torque is transmitted to the block through the light pulley, causing it to accelerate.
Step 1: Calculate the torque exerted on the wheel.
τ = Fr
τ = (ma)r
τ = mar
Step 2: Calculate the angular acceleration of the wheel.
τ = Iα
mar = Iα
α = (mar) / I
Step 3: Convert the linear acceleration of the block to angular acceleration.
The linear acceleration of the block is the same as the angular acceleration of the wheel because they are connected by the string.
So, α = a / r
Step 4: Substitute the value of α in the previous equation.
a / r = (mar) / I
Step 5: Solve for the acceleration of the block (a).
a = (mar^2) / I
Step 6: Substitute the given values into the equation and calculate the acceleration.
a = (2 * 0.1 * 0.1^2) / 0.20
a = 0.01 m/s^2
Answer:
The acceleration of the block is 0.01 m/s^2.
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A string is wrapped on a wheel of moment of inertia o.20kg m^2and radius10cm and goes through a light pulley to support a block of mass 2kg. Find the acceleration of the block?
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A string is wrapped on a wheel of moment of inertia o.20kg m^2and radius10cm and goes through a light pulley to support a block of mass 2kg. Find the acceleration of the block? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A string is wrapped on a wheel of moment of inertia o.20kg m^2and radius10cm and goes through a light pulley to support a block of mass 2kg. Find the acceleration of the block? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A string is wrapped on a wheel of moment of inertia o.20kg m^2and radius10cm and goes through a light pulley to support a block of mass 2kg. Find the acceleration of the block?.
A string is wrapped on a wheel of moment of inertia o.20kg m^2and radius10cm and goes through a light pulley to support a block of mass 2kg. Find the acceleration of the block? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A string is wrapped on a wheel of moment of inertia o.20kg m^2and radius10cm and goes through a light pulley to support a block of mass 2kg. Find the acceleration of the block? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A string is wrapped on a wheel of moment of inertia o.20kg m^2and radius10cm and goes through a light pulley to support a block of mass 2kg. Find the acceleration of the block?.
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