363193
In the given figure, \(a = 15\,\,{\rm{m/}}{{\rm{s}}^{\rm{2}}}\) represents the total acceleration of a particle moving in the clockwise direction in a circle of radius \(R = 2.5\,m\) at a given instant of time. The speed of the particle is
363194
A coin placed on a rotating turn table just slips, if it is placed at a distance of \(8\;cm\) from the centre. If angular speed of the turn table is doubled, then it will just slip at a distance of
1 \(1\;cm\)
2 \(2\;cm\)
3 \(4\;cm\)
4 \(8\;cm\)
Explanation:
A body placed on a non-inertial frame of reference which is rotating about its axis, experiences a centrifugal force. It is given by \(F=m r \omega^{2}\) where, \(r\) is radius of circle, \(m\) is mass and \(\omega\) is angular speed. \(\therefore \dfrac{F_{1}}{F_{2}}=\dfrac{r_{1} \omega_{1}^{2}}{r_{2} \omega_{2}^{2}}\) Since, \(F_{1}=F_{2}\) \(\Rightarrow r_{1} \omega_{1}^{2}=r_{2} \omega_{2}^{2}\) \(\Rightarrow \quad r_{2}=\dfrac{r_{1} \omega_{1}^{2}}{\omega_{2}^{2}}\) Given, \(r_{1}=8 \mathrm{~cm}, \omega_{1}=\omega\) and \(\omega_{2}=2 \omega\) \(\therefore \quad {r_2} = \frac{{8 \times {\omega ^2}}}{{{{(2\omega )}^2}}} = \frac{8}{4} = 2\;cm\)
PHXI05:LAWS OF MOTION
363195
A stone of mass \(250\,g\) is tied to the end of a string of length \(1.0\,m\). It is whirled in a horizontal circle on a smooth plane with a frequency of \(30{\text{ }}rev/\min .\) What is the tension in the string?
1 \({\dfrac{\pi^{2}}{4} N}\)
2 \({\dfrac{\pi^{2}}{6} N}\)
3 \({4 \pi^{2} N}\)
4 \({2 \pi^{2} N}\)
Explanation:
Mass of the stone \({=250 {~g}=\dfrac{250 {~kg}}{1000}=\dfrac{1}{4} {~kg}}\) \({T=m \omega^{2} r=\dfrac{1}{4} \times\left(\dfrac{2 \pi \times 30}{60}\right)^{2} \times 1=\dfrac{\pi^{2}}{4} N}\)
PHXI05:LAWS OF MOTION
363196
Assertion : When a vehicle takes a turn on the road, it travels along a nearly circular path. Reason : In circular motion, velocity of vehicle remains same.
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:
In circular motion, the frictional force acts toward the center of the horizontal circular path, providing the necessary centripetal force to prevent the vehicle from overturning. This is because in circular motion, there is a change in the direction of motion, leading to a change in velocity. So correct option is (3)
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PHXI05:LAWS OF MOTION
363193
In the given figure, \(a = 15\,\,{\rm{m/}}{{\rm{s}}^{\rm{2}}}\) represents the total acceleration of a particle moving in the clockwise direction in a circle of radius \(R = 2.5\,m\) at a given instant of time. The speed of the particle is
363194
A coin placed on a rotating turn table just slips, if it is placed at a distance of \(8\;cm\) from the centre. If angular speed of the turn table is doubled, then it will just slip at a distance of
1 \(1\;cm\)
2 \(2\;cm\)
3 \(4\;cm\)
4 \(8\;cm\)
Explanation:
A body placed on a non-inertial frame of reference which is rotating about its axis, experiences a centrifugal force. It is given by \(F=m r \omega^{2}\) where, \(r\) is radius of circle, \(m\) is mass and \(\omega\) is angular speed. \(\therefore \dfrac{F_{1}}{F_{2}}=\dfrac{r_{1} \omega_{1}^{2}}{r_{2} \omega_{2}^{2}}\) Since, \(F_{1}=F_{2}\) \(\Rightarrow r_{1} \omega_{1}^{2}=r_{2} \omega_{2}^{2}\) \(\Rightarrow \quad r_{2}=\dfrac{r_{1} \omega_{1}^{2}}{\omega_{2}^{2}}\) Given, \(r_{1}=8 \mathrm{~cm}, \omega_{1}=\omega\) and \(\omega_{2}=2 \omega\) \(\therefore \quad {r_2} = \frac{{8 \times {\omega ^2}}}{{{{(2\omega )}^2}}} = \frac{8}{4} = 2\;cm\)
PHXI05:LAWS OF MOTION
363195
A stone of mass \(250\,g\) is tied to the end of a string of length \(1.0\,m\). It is whirled in a horizontal circle on a smooth plane with a frequency of \(30{\text{ }}rev/\min .\) What is the tension in the string?
1 \({\dfrac{\pi^{2}}{4} N}\)
2 \({\dfrac{\pi^{2}}{6} N}\)
3 \({4 \pi^{2} N}\)
4 \({2 \pi^{2} N}\)
Explanation:
Mass of the stone \({=250 {~g}=\dfrac{250 {~kg}}{1000}=\dfrac{1}{4} {~kg}}\) \({T=m \omega^{2} r=\dfrac{1}{4} \times\left(\dfrac{2 \pi \times 30}{60}\right)^{2} \times 1=\dfrac{\pi^{2}}{4} N}\)
PHXI05:LAWS OF MOTION
363196
Assertion : When a vehicle takes a turn on the road, it travels along a nearly circular path. Reason : In circular motion, velocity of vehicle remains same.
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:
In circular motion, the frictional force acts toward the center of the horizontal circular path, providing the necessary centripetal force to prevent the vehicle from overturning. This is because in circular motion, there is a change in the direction of motion, leading to a change in velocity. So correct option is (3)
363193
In the given figure, \(a = 15\,\,{\rm{m/}}{{\rm{s}}^{\rm{2}}}\) represents the total acceleration of a particle moving in the clockwise direction in a circle of radius \(R = 2.5\,m\) at a given instant of time. The speed of the particle is
363194
A coin placed on a rotating turn table just slips, if it is placed at a distance of \(8\;cm\) from the centre. If angular speed of the turn table is doubled, then it will just slip at a distance of
1 \(1\;cm\)
2 \(2\;cm\)
3 \(4\;cm\)
4 \(8\;cm\)
Explanation:
A body placed on a non-inertial frame of reference which is rotating about its axis, experiences a centrifugal force. It is given by \(F=m r \omega^{2}\) where, \(r\) is radius of circle, \(m\) is mass and \(\omega\) is angular speed. \(\therefore \dfrac{F_{1}}{F_{2}}=\dfrac{r_{1} \omega_{1}^{2}}{r_{2} \omega_{2}^{2}}\) Since, \(F_{1}=F_{2}\) \(\Rightarrow r_{1} \omega_{1}^{2}=r_{2} \omega_{2}^{2}\) \(\Rightarrow \quad r_{2}=\dfrac{r_{1} \omega_{1}^{2}}{\omega_{2}^{2}}\) Given, \(r_{1}=8 \mathrm{~cm}, \omega_{1}=\omega\) and \(\omega_{2}=2 \omega\) \(\therefore \quad {r_2} = \frac{{8 \times {\omega ^2}}}{{{{(2\omega )}^2}}} = \frac{8}{4} = 2\;cm\)
PHXI05:LAWS OF MOTION
363195
A stone of mass \(250\,g\) is tied to the end of a string of length \(1.0\,m\). It is whirled in a horizontal circle on a smooth plane with a frequency of \(30{\text{ }}rev/\min .\) What is the tension in the string?
1 \({\dfrac{\pi^{2}}{4} N}\)
2 \({\dfrac{\pi^{2}}{6} N}\)
3 \({4 \pi^{2} N}\)
4 \({2 \pi^{2} N}\)
Explanation:
Mass of the stone \({=250 {~g}=\dfrac{250 {~kg}}{1000}=\dfrac{1}{4} {~kg}}\) \({T=m \omega^{2} r=\dfrac{1}{4} \times\left(\dfrac{2 \pi \times 30}{60}\right)^{2} \times 1=\dfrac{\pi^{2}}{4} N}\)
PHXI05:LAWS OF MOTION
363196
Assertion : When a vehicle takes a turn on the road, it travels along a nearly circular path. Reason : In circular motion, velocity of vehicle remains same.
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:
In circular motion, the frictional force acts toward the center of the horizontal circular path, providing the necessary centripetal force to prevent the vehicle from overturning. This is because in circular motion, there is a change in the direction of motion, leading to a change in velocity. So correct option is (3)
363193
In the given figure, \(a = 15\,\,{\rm{m/}}{{\rm{s}}^{\rm{2}}}\) represents the total acceleration of a particle moving in the clockwise direction in a circle of radius \(R = 2.5\,m\) at a given instant of time. The speed of the particle is
363194
A coin placed on a rotating turn table just slips, if it is placed at a distance of \(8\;cm\) from the centre. If angular speed of the turn table is doubled, then it will just slip at a distance of
1 \(1\;cm\)
2 \(2\;cm\)
3 \(4\;cm\)
4 \(8\;cm\)
Explanation:
A body placed on a non-inertial frame of reference which is rotating about its axis, experiences a centrifugal force. It is given by \(F=m r \omega^{2}\) where, \(r\) is radius of circle, \(m\) is mass and \(\omega\) is angular speed. \(\therefore \dfrac{F_{1}}{F_{2}}=\dfrac{r_{1} \omega_{1}^{2}}{r_{2} \omega_{2}^{2}}\) Since, \(F_{1}=F_{2}\) \(\Rightarrow r_{1} \omega_{1}^{2}=r_{2} \omega_{2}^{2}\) \(\Rightarrow \quad r_{2}=\dfrac{r_{1} \omega_{1}^{2}}{\omega_{2}^{2}}\) Given, \(r_{1}=8 \mathrm{~cm}, \omega_{1}=\omega\) and \(\omega_{2}=2 \omega\) \(\therefore \quad {r_2} = \frac{{8 \times {\omega ^2}}}{{{{(2\omega )}^2}}} = \frac{8}{4} = 2\;cm\)
PHXI05:LAWS OF MOTION
363195
A stone of mass \(250\,g\) is tied to the end of a string of length \(1.0\,m\). It is whirled in a horizontal circle on a smooth plane with a frequency of \(30{\text{ }}rev/\min .\) What is the tension in the string?
1 \({\dfrac{\pi^{2}}{4} N}\)
2 \({\dfrac{\pi^{2}}{6} N}\)
3 \({4 \pi^{2} N}\)
4 \({2 \pi^{2} N}\)
Explanation:
Mass of the stone \({=250 {~g}=\dfrac{250 {~kg}}{1000}=\dfrac{1}{4} {~kg}}\) \({T=m \omega^{2} r=\dfrac{1}{4} \times\left(\dfrac{2 \pi \times 30}{60}\right)^{2} \times 1=\dfrac{\pi^{2}}{4} N}\)
PHXI05:LAWS OF MOTION
363196
Assertion : When a vehicle takes a turn on the road, it travels along a nearly circular path. Reason : In circular motion, velocity of vehicle remains same.
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:
In circular motion, the frictional force acts toward the center of the horizontal circular path, providing the necessary centripetal force to prevent the vehicle from overturning. This is because in circular motion, there is a change in the direction of motion, leading to a change in velocity. So correct option is (3)
