361904
Assertion : If the speed of a body is constant, the body cannot have a path other than a circular or straight line path. Reason : It is possible for a body to have a constant speed in an accelerated motion.
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:
When the speed of a body is constant, it can follow a variety of curved paths. With zero acceleration, the body moves at a constant speed along a straight line. In cases where the magnitude of acceleration remains constant but its direction continuously changes to stay perpendicular to the motion, the body moves at a constant speed along a circular path. So assertion is wrong. Uniform circular motion, for instance, involves a body moving at a constant speed while its direction continually changes, resulting in a non-zero acceleration. So correct option is (4).
PHXI04:MOTION IN A PLANE
361905
The difference between angular speed of minute hand and second hand of a clock is
1 \(\frac{{59\pi }}{{900}}rad/s\)
2 \(\frac{{59\pi }}{{1800}}rad/s\)
3 \(\frac{{59\pi }}{{2400}}rad/s\)
4 \(\frac{{59\pi }}{{3600}}rad/s\)
Explanation:
Angular speed of minute hand, \({\omega _m} = 2\pi \) radian per hour \( = \frac{{2\pi }}{{3600}}rad/s\) Angular speed of second hand, \({\omega _s} = 2\pi \) radian per minute \( = \frac{{2\pi }}{{60}}rad/s\) \(\therefore \) Difference between angular speeds of minute hand and second hand of a clock \( = {\omega _{\rm{s}}} - {\omega _{\rm{m}}} = \frac{{2\pi }}{{60}} - \frac{{2\pi }}{{3600}} = \frac{{59\pi }}{{1800}}{\rm{rad/s}}\)
MHTCET - 2015
PHXI04:MOTION IN A PLANE
361906
A body is moving in a circular path with acceleration a. If its velocity gets doubled, find the ratio of acceleration after and before the change
1 \({1: 4}\)
2 \({4: 1}\)
3 \({2: 1}\)
4 \(1:2\)
Explanation:
In a circular motion, \({a=\dfrac{v^{2}}{r}}\) \({\therefore \quad \dfrac{a_{2}}{a_{1}}=\left(\dfrac{v_{2}}{v_{1}}\right)^{2}}\) \( = {\left( {\frac{{2{v_1}}}{{{v_1}}}} \right)^2} = 4\,\,\,i.\,e.\,\,\,4:1\)
PHXI04:MOTION IN A PLANE
361907
A car runs around the curve of radius 0.3 \(km\) at a constant speed of \(60\,m{s^{ - 1}}\). The resultant change in velocity, instantaneous acceleration and average acceleration over \(60^\circ \) arc are
361904
Assertion : If the speed of a body is constant, the body cannot have a path other than a circular or straight line path. Reason : It is possible for a body to have a constant speed in an accelerated motion.
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:
When the speed of a body is constant, it can follow a variety of curved paths. With zero acceleration, the body moves at a constant speed along a straight line. In cases where the magnitude of acceleration remains constant but its direction continuously changes to stay perpendicular to the motion, the body moves at a constant speed along a circular path. So assertion is wrong. Uniform circular motion, for instance, involves a body moving at a constant speed while its direction continually changes, resulting in a non-zero acceleration. So correct option is (4).
PHXI04:MOTION IN A PLANE
361905
The difference between angular speed of minute hand and second hand of a clock is
1 \(\frac{{59\pi }}{{900}}rad/s\)
2 \(\frac{{59\pi }}{{1800}}rad/s\)
3 \(\frac{{59\pi }}{{2400}}rad/s\)
4 \(\frac{{59\pi }}{{3600}}rad/s\)
Explanation:
Angular speed of minute hand, \({\omega _m} = 2\pi \) radian per hour \( = \frac{{2\pi }}{{3600}}rad/s\) Angular speed of second hand, \({\omega _s} = 2\pi \) radian per minute \( = \frac{{2\pi }}{{60}}rad/s\) \(\therefore \) Difference between angular speeds of minute hand and second hand of a clock \( = {\omega _{\rm{s}}} - {\omega _{\rm{m}}} = \frac{{2\pi }}{{60}} - \frac{{2\pi }}{{3600}} = \frac{{59\pi }}{{1800}}{\rm{rad/s}}\)
MHTCET - 2015
PHXI04:MOTION IN A PLANE
361906
A body is moving in a circular path with acceleration a. If its velocity gets doubled, find the ratio of acceleration after and before the change
1 \({1: 4}\)
2 \({4: 1}\)
3 \({2: 1}\)
4 \(1:2\)
Explanation:
In a circular motion, \({a=\dfrac{v^{2}}{r}}\) \({\therefore \quad \dfrac{a_{2}}{a_{1}}=\left(\dfrac{v_{2}}{v_{1}}\right)^{2}}\) \( = {\left( {\frac{{2{v_1}}}{{{v_1}}}} \right)^2} = 4\,\,\,i.\,e.\,\,\,4:1\)
PHXI04:MOTION IN A PLANE
361907
A car runs around the curve of radius 0.3 \(km\) at a constant speed of \(60\,m{s^{ - 1}}\). The resultant change in velocity, instantaneous acceleration and average acceleration over \(60^\circ \) arc are
361904
Assertion : If the speed of a body is constant, the body cannot have a path other than a circular or straight line path. Reason : It is possible for a body to have a constant speed in an accelerated motion.
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:
When the speed of a body is constant, it can follow a variety of curved paths. With zero acceleration, the body moves at a constant speed along a straight line. In cases where the magnitude of acceleration remains constant but its direction continuously changes to stay perpendicular to the motion, the body moves at a constant speed along a circular path. So assertion is wrong. Uniform circular motion, for instance, involves a body moving at a constant speed while its direction continually changes, resulting in a non-zero acceleration. So correct option is (4).
PHXI04:MOTION IN A PLANE
361905
The difference between angular speed of minute hand and second hand of a clock is
1 \(\frac{{59\pi }}{{900}}rad/s\)
2 \(\frac{{59\pi }}{{1800}}rad/s\)
3 \(\frac{{59\pi }}{{2400}}rad/s\)
4 \(\frac{{59\pi }}{{3600}}rad/s\)
Explanation:
Angular speed of minute hand, \({\omega _m} = 2\pi \) radian per hour \( = \frac{{2\pi }}{{3600}}rad/s\) Angular speed of second hand, \({\omega _s} = 2\pi \) radian per minute \( = \frac{{2\pi }}{{60}}rad/s\) \(\therefore \) Difference between angular speeds of minute hand and second hand of a clock \( = {\omega _{\rm{s}}} - {\omega _{\rm{m}}} = \frac{{2\pi }}{{60}} - \frac{{2\pi }}{{3600}} = \frac{{59\pi }}{{1800}}{\rm{rad/s}}\)
MHTCET - 2015
PHXI04:MOTION IN A PLANE
361906
A body is moving in a circular path with acceleration a. If its velocity gets doubled, find the ratio of acceleration after and before the change
1 \({1: 4}\)
2 \({4: 1}\)
3 \({2: 1}\)
4 \(1:2\)
Explanation:
In a circular motion, \({a=\dfrac{v^{2}}{r}}\) \({\therefore \quad \dfrac{a_{2}}{a_{1}}=\left(\dfrac{v_{2}}{v_{1}}\right)^{2}}\) \( = {\left( {\frac{{2{v_1}}}{{{v_1}}}} \right)^2} = 4\,\,\,i.\,e.\,\,\,4:1\)
PHXI04:MOTION IN A PLANE
361907
A car runs around the curve of radius 0.3 \(km\) at a constant speed of \(60\,m{s^{ - 1}}\). The resultant change in velocity, instantaneous acceleration and average acceleration over \(60^\circ \) arc are
361904
Assertion : If the speed of a body is constant, the body cannot have a path other than a circular or straight line path. Reason : It is possible for a body to have a constant speed in an accelerated motion.
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:
When the speed of a body is constant, it can follow a variety of curved paths. With zero acceleration, the body moves at a constant speed along a straight line. In cases where the magnitude of acceleration remains constant but its direction continuously changes to stay perpendicular to the motion, the body moves at a constant speed along a circular path. So assertion is wrong. Uniform circular motion, for instance, involves a body moving at a constant speed while its direction continually changes, resulting in a non-zero acceleration. So correct option is (4).
PHXI04:MOTION IN A PLANE
361905
The difference between angular speed of minute hand and second hand of a clock is
1 \(\frac{{59\pi }}{{900}}rad/s\)
2 \(\frac{{59\pi }}{{1800}}rad/s\)
3 \(\frac{{59\pi }}{{2400}}rad/s\)
4 \(\frac{{59\pi }}{{3600}}rad/s\)
Explanation:
Angular speed of minute hand, \({\omega _m} = 2\pi \) radian per hour \( = \frac{{2\pi }}{{3600}}rad/s\) Angular speed of second hand, \({\omega _s} = 2\pi \) radian per minute \( = \frac{{2\pi }}{{60}}rad/s\) \(\therefore \) Difference between angular speeds of minute hand and second hand of a clock \( = {\omega _{\rm{s}}} - {\omega _{\rm{m}}} = \frac{{2\pi }}{{60}} - \frac{{2\pi }}{{3600}} = \frac{{59\pi }}{{1800}}{\rm{rad/s}}\)
MHTCET - 2015
PHXI04:MOTION IN A PLANE
361906
A body is moving in a circular path with acceleration a. If its velocity gets doubled, find the ratio of acceleration after and before the change
1 \({1: 4}\)
2 \({4: 1}\)
3 \({2: 1}\)
4 \(1:2\)
Explanation:
In a circular motion, \({a=\dfrac{v^{2}}{r}}\) \({\therefore \quad \dfrac{a_{2}}{a_{1}}=\left(\dfrac{v_{2}}{v_{1}}\right)^{2}}\) \( = {\left( {\frac{{2{v_1}}}{{{v_1}}}} \right)^2} = 4\,\,\,i.\,e.\,\,\,4:1\)
PHXI04:MOTION IN A PLANE
361907
A car runs around the curve of radius 0.3 \(km\) at a constant speed of \(60\,m{s^{ - 1}}\). The resultant change in velocity, instantaneous acceleration and average acceleration over \(60^\circ \) arc are
