355702
The velocity of a body moving in a vertical circle of radius \(r\) is \(\sqrt{7 g r}\) at the lowest point of the circle. What is the ratio of maximum and minimum tension?
1 \(4: 1\)
2 \(\sqrt{7}: 1\)
3 \(3: 1\)
4 \(2: 1\)
Explanation:
Tension is maximum at the lowest point and minimum at the highest point. Tension at the lowest point, \({T_L} = mg + \frac{{mv_L^2}}{r} = mg + \frac{{7mgr}}{r}\) \(\left( {\because {v_L} = \sqrt {7gr} } \right)\) \({T_L} = 8\,mg\) \(As\,{T_L} - {T_H} = 6mg\) \(\therefore {T_H} = {T_L} - 6mg = 8mg - 6mg = 2mg\) \(\therefore \frac{{{T_L}}}{{{T_H}}} = \frac{4}{1}\,or\,\frac{{{T_{\max }}}}{{{T_{\min }}}} = \frac{4}{1}\)
PHXI06:WORK ENERGY AND POWER
355703
A frictionless track \(A B C D E\) ends in a circular loop of radius \(R\). A body slides down the track from point \(A\) which is at a height \(h=5 \mathrm{~cm}\). Maximum value of \(R\) for the body to successfully complete the loop is
1 \(\frac{{15}}{4}cm\)
2 \(5\,cm\)
3 \(2\,cm\)
4 \(\frac{{10}}{3}cm\)
Explanation:
As the body moves on a circular track the body can complete vertical circular motion When the velocity at \(D\) is \(\sqrt{g R}\) From conservation of energy \(T \cdot {E_A} = T \cdot {E_D}mgh = mg(2R) + \frac{1}{2}m{(\sqrt {gR} )^2} \Rightarrow h = \frac{{5R}}{2}\) \( \Rightarrow R = \frac{{2h}}{5} = 2\;cm\) From the given options \({R_{\max }} = 2\;cm\)
PHXI06:WORK ENERGY AND POWER
355704
A vehicle is moving with uniform speed along horizontal, concave and convex surface roads. The surface on which, the normal reaction on the vehicle is maximum is
1 Concave
2 Convex
3 Horizontal
4 Same at all surfaces
Explanation:
Conceptual Question
PHXI06:WORK ENERGY AND POWER
355705
A car is moving up with uniform speed along a concave bridge which is part of a vertical circle. The true statement from the following is
1 Normal reaction on the car gradually decreases and becomes minimum at lowest position of bridge
2 Normal reaction on the car gradually increases and becomes maximum at lowest position
3 Normal reaction on car does not change
4 Normal reaction on the car gradually decreases and becomes zero at lowest position
355702
The velocity of a body moving in a vertical circle of radius \(r\) is \(\sqrt{7 g r}\) at the lowest point of the circle. What is the ratio of maximum and minimum tension?
1 \(4: 1\)
2 \(\sqrt{7}: 1\)
3 \(3: 1\)
4 \(2: 1\)
Explanation:
Tension is maximum at the lowest point and minimum at the highest point. Tension at the lowest point, \({T_L} = mg + \frac{{mv_L^2}}{r} = mg + \frac{{7mgr}}{r}\) \(\left( {\because {v_L} = \sqrt {7gr} } \right)\) \({T_L} = 8\,mg\) \(As\,{T_L} - {T_H} = 6mg\) \(\therefore {T_H} = {T_L} - 6mg = 8mg - 6mg = 2mg\) \(\therefore \frac{{{T_L}}}{{{T_H}}} = \frac{4}{1}\,or\,\frac{{{T_{\max }}}}{{{T_{\min }}}} = \frac{4}{1}\)
PHXI06:WORK ENERGY AND POWER
355703
A frictionless track \(A B C D E\) ends in a circular loop of radius \(R\). A body slides down the track from point \(A\) which is at a height \(h=5 \mathrm{~cm}\). Maximum value of \(R\) for the body to successfully complete the loop is
1 \(\frac{{15}}{4}cm\)
2 \(5\,cm\)
3 \(2\,cm\)
4 \(\frac{{10}}{3}cm\)
Explanation:
As the body moves on a circular track the body can complete vertical circular motion When the velocity at \(D\) is \(\sqrt{g R}\) From conservation of energy \(T \cdot {E_A} = T \cdot {E_D}mgh = mg(2R) + \frac{1}{2}m{(\sqrt {gR} )^2} \Rightarrow h = \frac{{5R}}{2}\) \( \Rightarrow R = \frac{{2h}}{5} = 2\;cm\) From the given options \({R_{\max }} = 2\;cm\)
PHXI06:WORK ENERGY AND POWER
355704
A vehicle is moving with uniform speed along horizontal, concave and convex surface roads. The surface on which, the normal reaction on the vehicle is maximum is
1 Concave
2 Convex
3 Horizontal
4 Same at all surfaces
Explanation:
Conceptual Question
PHXI06:WORK ENERGY AND POWER
355705
A car is moving up with uniform speed along a concave bridge which is part of a vertical circle. The true statement from the following is
1 Normal reaction on the car gradually decreases and becomes minimum at lowest position of bridge
2 Normal reaction on the car gradually increases and becomes maximum at lowest position
3 Normal reaction on car does not change
4 Normal reaction on the car gradually decreases and becomes zero at lowest position
355702
The velocity of a body moving in a vertical circle of radius \(r\) is \(\sqrt{7 g r}\) at the lowest point of the circle. What is the ratio of maximum and minimum tension?
1 \(4: 1\)
2 \(\sqrt{7}: 1\)
3 \(3: 1\)
4 \(2: 1\)
Explanation:
Tension is maximum at the lowest point and minimum at the highest point. Tension at the lowest point, \({T_L} = mg + \frac{{mv_L^2}}{r} = mg + \frac{{7mgr}}{r}\) \(\left( {\because {v_L} = \sqrt {7gr} } \right)\) \({T_L} = 8\,mg\) \(As\,{T_L} - {T_H} = 6mg\) \(\therefore {T_H} = {T_L} - 6mg = 8mg - 6mg = 2mg\) \(\therefore \frac{{{T_L}}}{{{T_H}}} = \frac{4}{1}\,or\,\frac{{{T_{\max }}}}{{{T_{\min }}}} = \frac{4}{1}\)
PHXI06:WORK ENERGY AND POWER
355703
A frictionless track \(A B C D E\) ends in a circular loop of radius \(R\). A body slides down the track from point \(A\) which is at a height \(h=5 \mathrm{~cm}\). Maximum value of \(R\) for the body to successfully complete the loop is
1 \(\frac{{15}}{4}cm\)
2 \(5\,cm\)
3 \(2\,cm\)
4 \(\frac{{10}}{3}cm\)
Explanation:
As the body moves on a circular track the body can complete vertical circular motion When the velocity at \(D\) is \(\sqrt{g R}\) From conservation of energy \(T \cdot {E_A} = T \cdot {E_D}mgh = mg(2R) + \frac{1}{2}m{(\sqrt {gR} )^2} \Rightarrow h = \frac{{5R}}{2}\) \( \Rightarrow R = \frac{{2h}}{5} = 2\;cm\) From the given options \({R_{\max }} = 2\;cm\)
PHXI06:WORK ENERGY AND POWER
355704
A vehicle is moving with uniform speed along horizontal, concave and convex surface roads. The surface on which, the normal reaction on the vehicle is maximum is
1 Concave
2 Convex
3 Horizontal
4 Same at all surfaces
Explanation:
Conceptual Question
PHXI06:WORK ENERGY AND POWER
355705
A car is moving up with uniform speed along a concave bridge which is part of a vertical circle. The true statement from the following is
1 Normal reaction on the car gradually decreases and becomes minimum at lowest position of bridge
2 Normal reaction on the car gradually increases and becomes maximum at lowest position
3 Normal reaction on car does not change
4 Normal reaction on the car gradually decreases and becomes zero at lowest position
355702
The velocity of a body moving in a vertical circle of radius \(r\) is \(\sqrt{7 g r}\) at the lowest point of the circle. What is the ratio of maximum and minimum tension?
1 \(4: 1\)
2 \(\sqrt{7}: 1\)
3 \(3: 1\)
4 \(2: 1\)
Explanation:
Tension is maximum at the lowest point and minimum at the highest point. Tension at the lowest point, \({T_L} = mg + \frac{{mv_L^2}}{r} = mg + \frac{{7mgr}}{r}\) \(\left( {\because {v_L} = \sqrt {7gr} } \right)\) \({T_L} = 8\,mg\) \(As\,{T_L} - {T_H} = 6mg\) \(\therefore {T_H} = {T_L} - 6mg = 8mg - 6mg = 2mg\) \(\therefore \frac{{{T_L}}}{{{T_H}}} = \frac{4}{1}\,or\,\frac{{{T_{\max }}}}{{{T_{\min }}}} = \frac{4}{1}\)
PHXI06:WORK ENERGY AND POWER
355703
A frictionless track \(A B C D E\) ends in a circular loop of radius \(R\). A body slides down the track from point \(A\) which is at a height \(h=5 \mathrm{~cm}\). Maximum value of \(R\) for the body to successfully complete the loop is
1 \(\frac{{15}}{4}cm\)
2 \(5\,cm\)
3 \(2\,cm\)
4 \(\frac{{10}}{3}cm\)
Explanation:
As the body moves on a circular track the body can complete vertical circular motion When the velocity at \(D\) is \(\sqrt{g R}\) From conservation of energy \(T \cdot {E_A} = T \cdot {E_D}mgh = mg(2R) + \frac{1}{2}m{(\sqrt {gR} )^2} \Rightarrow h = \frac{{5R}}{2}\) \( \Rightarrow R = \frac{{2h}}{5} = 2\;cm\) From the given options \({R_{\max }} = 2\;cm\)
PHXI06:WORK ENERGY AND POWER
355704
A vehicle is moving with uniform speed along horizontal, concave and convex surface roads. The surface on which, the normal reaction on the vehicle is maximum is
1 Concave
2 Convex
3 Horizontal
4 Same at all surfaces
Explanation:
Conceptual Question
PHXI06:WORK ENERGY AND POWER
355705
A car is moving up with uniform speed along a concave bridge which is part of a vertical circle. The true statement from the following is
1 Normal reaction on the car gradually decreases and becomes minimum at lowest position of bridge
2 Normal reaction on the car gradually increases and becomes maximum at lowest position
3 Normal reaction on car does not change
4 Normal reaction on the car gradually decreases and becomes zero at lowest position
