361865
A particle is going in a uniform helical and spiral path separately as shown in figure with constant speed.
1 The acceleration of the particle is constant in both cases.
2 The velocity of the particle is constant in both cases.
3 The magnitude of acceleration is decreasing continuously in both the cases.
4 The magnitude of acceleration is constant in (\(A\)) and decreasing in (\(B\)).
Explanation:
The magnitude of acceleration is contant in (\(A\)) and decreasing in (\(B\)). In (\(A\))\( \to \) \(r\) constant, \({a_t} = 0;\) \(v\) constant,\({a_t} = \frac{{{v^2}}}{R}\) constant In (\(B\))\( \to \) \(r\) is increasing, \(v\) constant \({a_t} = 0;{a_r} = \frac{{{v^2}}}{R}\) decreasing
PHXI04:MOTION IN A PLANE
361866
Assertion : The centripetal acceleration in circular motion is dependent on angular velocity of the body. Reason : When a particle moves in a circle with a uniform speed, its velocity and acceleration both changes.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The centripetal acceleration in circular motion is dependent on the square of the angular velocity, not just the angular velocity itself. While the velocity changes direction, its magnitude remains constant, resulting in a centripetal acceleration whose direction also changes. So correct option is (2).
PHXI04:MOTION IN A PLANE
361867
A particle is in uniform circular motion. Related to one complete revolution of the particle, which among the statements is incorrect?
1 Average speed of the particle is zero.
2 Average velocity of the particle is zero.
3 Average acceleration of the particle is zero.
4 Displacement of the particle is zero.
Explanation:
Speed is a scalar. \(\Rightarrow\) Average speed is non zero in circular motion. Correct option is (1).
KCET - 2023
PHXI04:MOTION IN A PLANE
361868
A car is travelling with linear velocity \(v\) on a circular road of radius \(R\). If its speed is increasing at the rate of \(a\;m{s^{ - 2}}\), then the net acceleration will be
1 \(\dfrac{v^{2}}{R}+a\)
2 \(\dfrac{v^{2}}{R}-a\)
3 \(\sqrt{\left(v^{2} / R\right)^{2}+a^{2}}\)
4 \(\sqrt{\left(v^{2} / R\right)^{2}-a^{2}}\)
Explanation:
Given speed is increasing at the rate of \(a\) \(m s^{-2}\). So, linear acceleration \(=a\) and tangential acceleration \(=v^{2} / R\) Hence, net acceleration \( = \sqrt {{{\left( {\frac{{{v^2}}}{R}} \right)}^2} + {a^2}} \)
AIIMS - 2013
PHXI04:MOTION IN A PLANE
361869
When a body moves in a circular path, with constant speed, no work is done by the force since,
1 There is no displacement
2 There is no net force
3 Force and displacement are perpendicular to each other
361865
A particle is going in a uniform helical and spiral path separately as shown in figure with constant speed.
1 The acceleration of the particle is constant in both cases.
2 The velocity of the particle is constant in both cases.
3 The magnitude of acceleration is decreasing continuously in both the cases.
4 The magnitude of acceleration is constant in (\(A\)) and decreasing in (\(B\)).
Explanation:
The magnitude of acceleration is contant in (\(A\)) and decreasing in (\(B\)). In (\(A\))\( \to \) \(r\) constant, \({a_t} = 0;\) \(v\) constant,\({a_t} = \frac{{{v^2}}}{R}\) constant In (\(B\))\( \to \) \(r\) is increasing, \(v\) constant \({a_t} = 0;{a_r} = \frac{{{v^2}}}{R}\) decreasing
PHXI04:MOTION IN A PLANE
361866
Assertion : The centripetal acceleration in circular motion is dependent on angular velocity of the body. Reason : When a particle moves in a circle with a uniform speed, its velocity and acceleration both changes.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The centripetal acceleration in circular motion is dependent on the square of the angular velocity, not just the angular velocity itself. While the velocity changes direction, its magnitude remains constant, resulting in a centripetal acceleration whose direction also changes. So correct option is (2).
PHXI04:MOTION IN A PLANE
361867
A particle is in uniform circular motion. Related to one complete revolution of the particle, which among the statements is incorrect?
1 Average speed of the particle is zero.
2 Average velocity of the particle is zero.
3 Average acceleration of the particle is zero.
4 Displacement of the particle is zero.
Explanation:
Speed is a scalar. \(\Rightarrow\) Average speed is non zero in circular motion. Correct option is (1).
KCET - 2023
PHXI04:MOTION IN A PLANE
361868
A car is travelling with linear velocity \(v\) on a circular road of radius \(R\). If its speed is increasing at the rate of \(a\;m{s^{ - 2}}\), then the net acceleration will be
1 \(\dfrac{v^{2}}{R}+a\)
2 \(\dfrac{v^{2}}{R}-a\)
3 \(\sqrt{\left(v^{2} / R\right)^{2}+a^{2}}\)
4 \(\sqrt{\left(v^{2} / R\right)^{2}-a^{2}}\)
Explanation:
Given speed is increasing at the rate of \(a\) \(m s^{-2}\). So, linear acceleration \(=a\) and tangential acceleration \(=v^{2} / R\) Hence, net acceleration \( = \sqrt {{{\left( {\frac{{{v^2}}}{R}} \right)}^2} + {a^2}} \)
AIIMS - 2013
PHXI04:MOTION IN A PLANE
361869
When a body moves in a circular path, with constant speed, no work is done by the force since,
1 There is no displacement
2 There is no net force
3 Force and displacement are perpendicular to each other
361865
A particle is going in a uniform helical and spiral path separately as shown in figure with constant speed.
1 The acceleration of the particle is constant in both cases.
2 The velocity of the particle is constant in both cases.
3 The magnitude of acceleration is decreasing continuously in both the cases.
4 The magnitude of acceleration is constant in (\(A\)) and decreasing in (\(B\)).
Explanation:
The magnitude of acceleration is contant in (\(A\)) and decreasing in (\(B\)). In (\(A\))\( \to \) \(r\) constant, \({a_t} = 0;\) \(v\) constant,\({a_t} = \frac{{{v^2}}}{R}\) constant In (\(B\))\( \to \) \(r\) is increasing, \(v\) constant \({a_t} = 0;{a_r} = \frac{{{v^2}}}{R}\) decreasing
PHXI04:MOTION IN A PLANE
361866
Assertion : The centripetal acceleration in circular motion is dependent on angular velocity of the body. Reason : When a particle moves in a circle with a uniform speed, its velocity and acceleration both changes.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The centripetal acceleration in circular motion is dependent on the square of the angular velocity, not just the angular velocity itself. While the velocity changes direction, its magnitude remains constant, resulting in a centripetal acceleration whose direction also changes. So correct option is (2).
PHXI04:MOTION IN A PLANE
361867
A particle is in uniform circular motion. Related to one complete revolution of the particle, which among the statements is incorrect?
1 Average speed of the particle is zero.
2 Average velocity of the particle is zero.
3 Average acceleration of the particle is zero.
4 Displacement of the particle is zero.
Explanation:
Speed is a scalar. \(\Rightarrow\) Average speed is non zero in circular motion. Correct option is (1).
KCET - 2023
PHXI04:MOTION IN A PLANE
361868
A car is travelling with linear velocity \(v\) on a circular road of radius \(R\). If its speed is increasing at the rate of \(a\;m{s^{ - 2}}\), then the net acceleration will be
1 \(\dfrac{v^{2}}{R}+a\)
2 \(\dfrac{v^{2}}{R}-a\)
3 \(\sqrt{\left(v^{2} / R\right)^{2}+a^{2}}\)
4 \(\sqrt{\left(v^{2} / R\right)^{2}-a^{2}}\)
Explanation:
Given speed is increasing at the rate of \(a\) \(m s^{-2}\). So, linear acceleration \(=a\) and tangential acceleration \(=v^{2} / R\) Hence, net acceleration \( = \sqrt {{{\left( {\frac{{{v^2}}}{R}} \right)}^2} + {a^2}} \)
AIIMS - 2013
PHXI04:MOTION IN A PLANE
361869
When a body moves in a circular path, with constant speed, no work is done by the force since,
1 There is no displacement
2 There is no net force
3 Force and displacement are perpendicular to each other
361865
A particle is going in a uniform helical and spiral path separately as shown in figure with constant speed.
1 The acceleration of the particle is constant in both cases.
2 The velocity of the particle is constant in both cases.
3 The magnitude of acceleration is decreasing continuously in both the cases.
4 The magnitude of acceleration is constant in (\(A\)) and decreasing in (\(B\)).
Explanation:
The magnitude of acceleration is contant in (\(A\)) and decreasing in (\(B\)). In (\(A\))\( \to \) \(r\) constant, \({a_t} = 0;\) \(v\) constant,\({a_t} = \frac{{{v^2}}}{R}\) constant In (\(B\))\( \to \) \(r\) is increasing, \(v\) constant \({a_t} = 0;{a_r} = \frac{{{v^2}}}{R}\) decreasing
PHXI04:MOTION IN A PLANE
361866
Assertion : The centripetal acceleration in circular motion is dependent on angular velocity of the body. Reason : When a particle moves in a circle with a uniform speed, its velocity and acceleration both changes.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The centripetal acceleration in circular motion is dependent on the square of the angular velocity, not just the angular velocity itself. While the velocity changes direction, its magnitude remains constant, resulting in a centripetal acceleration whose direction also changes. So correct option is (2).
PHXI04:MOTION IN A PLANE
361867
A particle is in uniform circular motion. Related to one complete revolution of the particle, which among the statements is incorrect?
1 Average speed of the particle is zero.
2 Average velocity of the particle is zero.
3 Average acceleration of the particle is zero.
4 Displacement of the particle is zero.
Explanation:
Speed is a scalar. \(\Rightarrow\) Average speed is non zero in circular motion. Correct option is (1).
KCET - 2023
PHXI04:MOTION IN A PLANE
361868
A car is travelling with linear velocity \(v\) on a circular road of radius \(R\). If its speed is increasing at the rate of \(a\;m{s^{ - 2}}\), then the net acceleration will be
1 \(\dfrac{v^{2}}{R}+a\)
2 \(\dfrac{v^{2}}{R}-a\)
3 \(\sqrt{\left(v^{2} / R\right)^{2}+a^{2}}\)
4 \(\sqrt{\left(v^{2} / R\right)^{2}-a^{2}}\)
Explanation:
Given speed is increasing at the rate of \(a\) \(m s^{-2}\). So, linear acceleration \(=a\) and tangential acceleration \(=v^{2} / R\) Hence, net acceleration \( = \sqrt {{{\left( {\frac{{{v^2}}}{R}} \right)}^2} + {a^2}} \)
AIIMS - 2013
PHXI04:MOTION IN A PLANE
361869
When a body moves in a circular path, with constant speed, no work is done by the force since,
1 There is no displacement
2 There is no net force
3 Force and displacement are perpendicular to each other
361865
A particle is going in a uniform helical and spiral path separately as shown in figure with constant speed.
1 The acceleration of the particle is constant in both cases.
2 The velocity of the particle is constant in both cases.
3 The magnitude of acceleration is decreasing continuously in both the cases.
4 The magnitude of acceleration is constant in (\(A\)) and decreasing in (\(B\)).
Explanation:
The magnitude of acceleration is contant in (\(A\)) and decreasing in (\(B\)). In (\(A\))\( \to \) \(r\) constant, \({a_t} = 0;\) \(v\) constant,\({a_t} = \frac{{{v^2}}}{R}\) constant In (\(B\))\( \to \) \(r\) is increasing, \(v\) constant \({a_t} = 0;{a_r} = \frac{{{v^2}}}{R}\) decreasing
PHXI04:MOTION IN A PLANE
361866
Assertion : The centripetal acceleration in circular motion is dependent on angular velocity of the body. Reason : When a particle moves in a circle with a uniform speed, its velocity and acceleration both changes.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The centripetal acceleration in circular motion is dependent on the square of the angular velocity, not just the angular velocity itself. While the velocity changes direction, its magnitude remains constant, resulting in a centripetal acceleration whose direction also changes. So correct option is (2).
PHXI04:MOTION IN A PLANE
361867
A particle is in uniform circular motion. Related to one complete revolution of the particle, which among the statements is incorrect?
1 Average speed of the particle is zero.
2 Average velocity of the particle is zero.
3 Average acceleration of the particle is zero.
4 Displacement of the particle is zero.
Explanation:
Speed is a scalar. \(\Rightarrow\) Average speed is non zero in circular motion. Correct option is (1).
KCET - 2023
PHXI04:MOTION IN A PLANE
361868
A car is travelling with linear velocity \(v\) on a circular road of radius \(R\). If its speed is increasing at the rate of \(a\;m{s^{ - 2}}\), then the net acceleration will be
1 \(\dfrac{v^{2}}{R}+a\)
2 \(\dfrac{v^{2}}{R}-a\)
3 \(\sqrt{\left(v^{2} / R\right)^{2}+a^{2}}\)
4 \(\sqrt{\left(v^{2} / R\right)^{2}-a^{2}}\)
Explanation:
Given speed is increasing at the rate of \(a\) \(m s^{-2}\). So, linear acceleration \(=a\) and tangential acceleration \(=v^{2} / R\) Hence, net acceleration \( = \sqrt {{{\left( {\frac{{{v^2}}}{R}} \right)}^2} + {a^2}} \)
AIIMS - 2013
PHXI04:MOTION IN A PLANE
361869
When a body moves in a circular path, with constant speed, no work is done by the force since,
1 There is no displacement
2 There is no net force
3 Force and displacement are perpendicular to each other
