The position vector of a particle R as a function of time t is given by
$\stackrel{\to }{\mathrm{R}}=4\mathrm{sin}\left[2\mathrm{\pi t}\right]\stackrel{^}{\mathrm{i}}+4\mathrm{cos}\left[2\mathrm{\pi t}\right]\stackrel{^}{\mathrm{j}}$
Where R is in meters, t is in seconds and  denote unit vectors along x and y-directions, respectively. Which one of the following statements is wrong for the motion of the particle?

1. Acceleration is along $-\stackrel{\to }{\mathrm{R}}$.

2. Magnitude of the acceleration vector is $\frac{{\mathrm{v}}^{2}}{\mathrm{R}}$, where v is the velocity of the particle.

3. Magnitude of the velocity of the particle is 8 m/s.

4. Path of the particle is a circle of radius 4m.

Subtopic:  Circular Motion |
To view explanation, please take trial in the course below.
NEET 2023 - Target Batch - Aryan Raj Singh
To view explanation, please take trial in the course below.
NEET 2023 - Target Batch - Aryan Raj Singh
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A particle moves in a circle of radius 5 cm with constant speed and time period $0.2\mathrm{\pi }$ sec. The acceleration of the particle is:

1.  25 m/s2

2.  36 m/s2

3.  5 m/s2

4.  15 m/s2

Subtopic:  Circular Motion |
To view explanation, please take trial in the course below.
NEET 2023 - Target Batch - Aryan Raj Singh
To view explanation, please take trial in the course below.
NEET 2023 - Target Batch - Aryan Raj Singh
Launched MCQ Practice Books

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A particle moves in the x – y plane according to the rule x = a sin ωt and y = a cos ωt. The particle follows:

1. a circular path.

2. a parabolic path.

3. a straight line path inclined equally to x and y-axes.

4. an elliptical path.

Subtopic:  Circular Motion |
To view explanation, please take trial in the course below.
NEET 2023 - Target Batch - Aryan Raj Singh
To view explanation, please take trial in the course below.
NEET 2023 - Target Batch - Aryan Raj Singh