Which of the following curves possibly represent one-dimensional motion of a particle?
A, B and D only
To determine which curves represent one-dimensional motion of a particle, we need to analyze each graph:
- Graph A: This graph shows a linear relationship between phase and time. - This can represent a particle undergoing simple harmonic motion, which is one-dimensional.
- Graph B: This graph is a circle on a velocity vs. displacement graph. - This can represent a sinusoidal or cyclic one-dimensional motion like circular motion with constant speed, projected onto one dimension. It implies a periodic one-dimensional motion.
- Graph C: This is a circular graph with velocity vs. time. - A circular graph in this context is not typically representative of one-dimensional motion since it suggests oscillation between positive and negative velocity implying non-linear motion in a higher dimension.
- Graph D: This graph shows a steady increase of total distance with time. - This indicates constant or monotonic motion, which is definitely one-dimensional.
By analyzing these graphs:
- A represents simple harmonic one-dimensional motion.
- B represents periodic one-dimensional motion.
- C does not represent one-dimensional motion.
- D represents one-dimensional motion because the total distance increases over time.
Therefore, the curves that represent one-dimensional motion are A, B, and D.
Correct Answer: A, B and D only.
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Important Questions from Mechanics
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Match the LIST-I with LIST-II
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A particle is released from height S above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.
The angle of projection of a particle is measured from the vertical axis as $\phi$ and the maximum height reached by the particle is $h_m$. Here $h_m$ as function of $\phi$ can be presented as
A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg, kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is
