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A small body is released from the rest on a fixed smooth inclined plane at t=0. Velocity versus time graph of the body us as shown in the figure. The angle of inclination of the plabe with the horizontal is?
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A small body is released from the rest on a fixed smooth inclined plan...
Here, we use the relation between the angles of inclination of particles to find the angle of inclination of the plane with the horizontal. Further, by substituting the given values we get the required result. Also, we will study the angle of inclination and basic frictional force, due to which an object cannot move smoothly.
Formula used:
As we know that the angle of inclination is an angle between the line and the x-axis.
Here, inclination a of the particle is given as:
Now, to find the angle of inclination of the plane with the horizontal we have the relation:
Here, θ is the required angle of inclination of the plane with the horizontal.
Substituting the given values in above equation we get:
Therefore, we get the required angle of inclination of plane with the horizontal i.e., θ=30∘.
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A small body is released from the rest on a fixed smooth inclined plan...
Analysis of the velocity-time graph
To determine the angle of inclination of the plane, we need to analyze the given velocity versus time graph of the body released from rest.
Understanding the graph
The graph shows that the velocity of the body increases linearly with time. This is evident from the fact that the graph is a straight line.
Interpreting the slope of the graph
The slope of the velocity-time graph represents the acceleration of the body. Since the velocity-time graph is a straight line, the acceleration is constant.
Calculating the acceleration
To calculate the acceleration, we can use the formula:
Acceleration (a) = Change in velocity / Change in time
From the graph, we can see that the change in velocity is given by the vertical difference between the initial and final velocities. The change in time is given by the horizontal difference between the initial and final times.
Determining the angle of inclination
The angle of inclination of the plane can be determined using the formula:
Acceleration (a) = g * sin(θ)
Where g is the acceleration due to gravity and θ is the angle of inclination.
From the previous step, we have calculated the acceleration. By substituting the known values into the formula and rearranging it, we can solve for the angle of inclination.
Conclusion
By analyzing the given velocity-time graph, we can calculate the acceleration of the body and then determine the angle of inclination of the plane. The angle of inclination can be found by rearranging the formula for acceleration and substituting the known values.
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A small body is released from the rest on a fixed smooth inclined plane at t=0. Velocity versus time graph of the body us as shown in the figure. The angle of inclination of the plabe with the horizontal is?
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A small body is released from the rest on a fixed smooth inclined plane at t=0. Velocity versus time graph of the body us as shown in the figure. The angle of inclination of the plabe with the horizontal is? 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 A small body is released from the rest on a fixed smooth inclined plane at t=0. Velocity versus time graph of the body us as shown in the figure. The angle of inclination of the plabe with the horizontal is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A small body is released from the rest on a fixed smooth inclined plane at t=0. Velocity versus time graph of the body us as shown in the figure. The angle of inclination of the plabe with the horizontal is?.
A small body is released from the rest on a fixed smooth inclined plane at t=0. Velocity versus time graph of the body us as shown in the figure. The angle of inclination of the plabe with the horizontal is? 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 A small body is released from the rest on a fixed smooth inclined plane at t=0. Velocity versus time graph of the body us as shown in the figure. The angle of inclination of the plabe with the horizontal is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A small body is released from the rest on a fixed smooth inclined plane at t=0. Velocity versus time graph of the body us as shown in the figure. The angle of inclination of the plabe with the horizontal is?.
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