Circular Motion
PHXI05:LAWS OF MOTION

363218 A hemispherical bowl of radius \(R\) is rotated about its axis of symmetry which is kept vertical with angular velocity \(\omega \). A small block is kept in the bowl. It remains stationary relative to the bowl surface at a position where the radius makes an angle \(\theta \) with the vertical. The friction is absent. The value of \(\theta \) is :-

1 \({\cos ^{ - 1}}\left( {\frac{g}{{R{\omega ^2}}}} \right)\)
2 \({\sin ^{ - 1}}\left( {\frac{g}{{R{\omega ^2}}}} \right)\)
3 \({\tan ^{ - 1}}\left( {\frac{g}{{R{\omega ^2}}}} \right)\)
4 \({\rm{None }}\,{\rm{of }}\,{\rm{these}}\)
PHXI05:LAWS OF MOTION

363219 A block of mass \(m\) is projected on a smooth horizontal circular track with velocity \(v\). What is the average normal force exerted by the circular walls on the block during its motion from \(A\) to \(B\)?
supporting img

1 \(\frac{{m{v^2}}}{R}\)
2 \(\frac{{m{v^2}}}{{\pi R}}\)
3 \(\frac{{2\,m{v^2}}}{R}\)
4 \(\frac{{2m{v^2}}}{{\pi R}}\)
PHXI05:LAWS OF MOTION

363220 A circular race track of radius 300 \(m\) is banked at an angle of \({\rm{15}}^\circ \) . If the coefficient of friction between the wheels of a race car and the road is 0.2, what is the maximum permissible speed to avoid slipping? (Take \({\rm{tan15}}^\circ = 0.27\))

1 \(38.2\,m{s^{ - 1}}\)
2 \(48.2\,m{s^{ - 1}}\)
3 \(18.2\,m{s^{ - 1}}\)
4 \(28.2\,m{s^{ - 1}}\)
PHXI05:LAWS OF MOTION

363221 A small block of mass \(1\,kg\) is held by a light string rests on a smooth inclined plane which can turn about \({Z Z^{\prime}}\)-axis with an angular velocity \(2\,rad/s\) as shown in the figure. The block is at distance \({\dfrac{1}{\sqrt{2}} {~m}}\) from the point \({O}\). The tension in the string is \({(32)^{x} {~N}}\). Find the value of \({x}\) is
supporting img

1 2
2 5
3 4
4 1
PHXI05:LAWS OF MOTION

363222 A person is driving a vehicle at uniform speed of \(5\,m{s^{ - 1}}\) on a level curved track of radius 5 \(m\). The coefficient of static friction between tyres and road is 0.1. Will the person slip while taking the turn with the same speed ? Take \(g = 10\,m{s^{ - 2}}\).
Choose the correct statement.

1 A person will slip if \({v^2} < 5{\mkern 1mu} {m^2}{s^{ - 2}}\)
2 A person will slip if \({v^2} = 5{\mkern 1mu} {m^2}{s^{ - 2}}\)
3 A person will not slip if \({v^2} > 10{\mkern 1mu} {m^2}{s^{ - 2}}\)
4 A person will slip if \({v^2} > 5{\mkern 1mu} {m^2}{s^{ - 2}}\)
PHXI05:LAWS OF MOTION

363218 A hemispherical bowl of radius \(R\) is rotated about its axis of symmetry which is kept vertical with angular velocity \(\omega \). A small block is kept in the bowl. It remains stationary relative to the bowl surface at a position where the radius makes an angle \(\theta \) with the vertical. The friction is absent. The value of \(\theta \) is :-

1 \({\cos ^{ - 1}}\left( {\frac{g}{{R{\omega ^2}}}} \right)\)
2 \({\sin ^{ - 1}}\left( {\frac{g}{{R{\omega ^2}}}} \right)\)
3 \({\tan ^{ - 1}}\left( {\frac{g}{{R{\omega ^2}}}} \right)\)
4 \({\rm{None }}\,{\rm{of }}\,{\rm{these}}\)
PHXI05:LAWS OF MOTION

363219 A block of mass \(m\) is projected on a smooth horizontal circular track with velocity \(v\). What is the average normal force exerted by the circular walls on the block during its motion from \(A\) to \(B\)?
supporting img

1 \(\frac{{m{v^2}}}{R}\)
2 \(\frac{{m{v^2}}}{{\pi R}}\)
3 \(\frac{{2\,m{v^2}}}{R}\)
4 \(\frac{{2m{v^2}}}{{\pi R}}\)
PHXI05:LAWS OF MOTION

363220 A circular race track of radius 300 \(m\) is banked at an angle of \({\rm{15}}^\circ \) . If the coefficient of friction between the wheels of a race car and the road is 0.2, what is the maximum permissible speed to avoid slipping? (Take \({\rm{tan15}}^\circ = 0.27\))

1 \(38.2\,m{s^{ - 1}}\)
2 \(48.2\,m{s^{ - 1}}\)
3 \(18.2\,m{s^{ - 1}}\)
4 \(28.2\,m{s^{ - 1}}\)
PHXI05:LAWS OF MOTION

363221 A small block of mass \(1\,kg\) is held by a light string rests on a smooth inclined plane which can turn about \({Z Z^{\prime}}\)-axis with an angular velocity \(2\,rad/s\) as shown in the figure. The block is at distance \({\dfrac{1}{\sqrt{2}} {~m}}\) from the point \({O}\). The tension in the string is \({(32)^{x} {~N}}\). Find the value of \({x}\) is
supporting img

1 2
2 5
3 4
4 1
PHXI05:LAWS OF MOTION

363222 A person is driving a vehicle at uniform speed of \(5\,m{s^{ - 1}}\) on a level curved track of radius 5 \(m\). The coefficient of static friction between tyres and road is 0.1. Will the person slip while taking the turn with the same speed ? Take \(g = 10\,m{s^{ - 2}}\).
Choose the correct statement.

1 A person will slip if \({v^2} < 5{\mkern 1mu} {m^2}{s^{ - 2}}\)
2 A person will slip if \({v^2} = 5{\mkern 1mu} {m^2}{s^{ - 2}}\)
3 A person will not slip if \({v^2} > 10{\mkern 1mu} {m^2}{s^{ - 2}}\)
4 A person will slip if \({v^2} > 5{\mkern 1mu} {m^2}{s^{ - 2}}\)
PHXI05:LAWS OF MOTION

363218 A hemispherical bowl of radius \(R\) is rotated about its axis of symmetry which is kept vertical with angular velocity \(\omega \). A small block is kept in the bowl. It remains stationary relative to the bowl surface at a position where the radius makes an angle \(\theta \) with the vertical. The friction is absent. The value of \(\theta \) is :-

1 \({\cos ^{ - 1}}\left( {\frac{g}{{R{\omega ^2}}}} \right)\)
2 \({\sin ^{ - 1}}\left( {\frac{g}{{R{\omega ^2}}}} \right)\)
3 \({\tan ^{ - 1}}\left( {\frac{g}{{R{\omega ^2}}}} \right)\)
4 \({\rm{None }}\,{\rm{of }}\,{\rm{these}}\)
PHXI05:LAWS OF MOTION

363219 A block of mass \(m\) is projected on a smooth horizontal circular track with velocity \(v\). What is the average normal force exerted by the circular walls on the block during its motion from \(A\) to \(B\)?
supporting img

1 \(\frac{{m{v^2}}}{R}\)
2 \(\frac{{m{v^2}}}{{\pi R}}\)
3 \(\frac{{2\,m{v^2}}}{R}\)
4 \(\frac{{2m{v^2}}}{{\pi R}}\)
PHXI05:LAWS OF MOTION

363220 A circular race track of radius 300 \(m\) is banked at an angle of \({\rm{15}}^\circ \) . If the coefficient of friction between the wheels of a race car and the road is 0.2, what is the maximum permissible speed to avoid slipping? (Take \({\rm{tan15}}^\circ = 0.27\))

1 \(38.2\,m{s^{ - 1}}\)
2 \(48.2\,m{s^{ - 1}}\)
3 \(18.2\,m{s^{ - 1}}\)
4 \(28.2\,m{s^{ - 1}}\)
PHXI05:LAWS OF MOTION

363221 A small block of mass \(1\,kg\) is held by a light string rests on a smooth inclined plane which can turn about \({Z Z^{\prime}}\)-axis with an angular velocity \(2\,rad/s\) as shown in the figure. The block is at distance \({\dfrac{1}{\sqrt{2}} {~m}}\) from the point \({O}\). The tension in the string is \({(32)^{x} {~N}}\). Find the value of \({x}\) is
supporting img

1 2
2 5
3 4
4 1
PHXI05:LAWS OF MOTION

363222 A person is driving a vehicle at uniform speed of \(5\,m{s^{ - 1}}\) on a level curved track of radius 5 \(m\). The coefficient of static friction between tyres and road is 0.1. Will the person slip while taking the turn with the same speed ? Take \(g = 10\,m{s^{ - 2}}\).
Choose the correct statement.

1 A person will slip if \({v^2} < 5{\mkern 1mu} {m^2}{s^{ - 2}}\)
2 A person will slip if \({v^2} = 5{\mkern 1mu} {m^2}{s^{ - 2}}\)
3 A person will not slip if \({v^2} > 10{\mkern 1mu} {m^2}{s^{ - 2}}\)
4 A person will slip if \({v^2} > 5{\mkern 1mu} {m^2}{s^{ - 2}}\)
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PHXI05:LAWS OF MOTION

363218 A hemispherical bowl of radius \(R\) is rotated about its axis of symmetry which is kept vertical with angular velocity \(\omega \). A small block is kept in the bowl. It remains stationary relative to the bowl surface at a position where the radius makes an angle \(\theta \) with the vertical. The friction is absent. The value of \(\theta \) is :-

1 \({\cos ^{ - 1}}\left( {\frac{g}{{R{\omega ^2}}}} \right)\)
2 \({\sin ^{ - 1}}\left( {\frac{g}{{R{\omega ^2}}}} \right)\)
3 \({\tan ^{ - 1}}\left( {\frac{g}{{R{\omega ^2}}}} \right)\)
4 \({\rm{None }}\,{\rm{of }}\,{\rm{these}}\)
PHXI05:LAWS OF MOTION

363219 A block of mass \(m\) is projected on a smooth horizontal circular track with velocity \(v\). What is the average normal force exerted by the circular walls on the block during its motion from \(A\) to \(B\)?
supporting img

1 \(\frac{{m{v^2}}}{R}\)
2 \(\frac{{m{v^2}}}{{\pi R}}\)
3 \(\frac{{2\,m{v^2}}}{R}\)
4 \(\frac{{2m{v^2}}}{{\pi R}}\)
PHXI05:LAWS OF MOTION

363220 A circular race track of radius 300 \(m\) is banked at an angle of \({\rm{15}}^\circ \) . If the coefficient of friction between the wheels of a race car and the road is 0.2, what is the maximum permissible speed to avoid slipping? (Take \({\rm{tan15}}^\circ = 0.27\))

1 \(38.2\,m{s^{ - 1}}\)
2 \(48.2\,m{s^{ - 1}}\)
3 \(18.2\,m{s^{ - 1}}\)
4 \(28.2\,m{s^{ - 1}}\)
PHXI05:LAWS OF MOTION

363221 A small block of mass \(1\,kg\) is held by a light string rests on a smooth inclined plane which can turn about \({Z Z^{\prime}}\)-axis with an angular velocity \(2\,rad/s\) as shown in the figure. The block is at distance \({\dfrac{1}{\sqrt{2}} {~m}}\) from the point \({O}\). The tension in the string is \({(32)^{x} {~N}}\). Find the value of \({x}\) is
supporting img

1 2
2 5
3 4
4 1
PHXI05:LAWS OF MOTION

363222 A person is driving a vehicle at uniform speed of \(5\,m{s^{ - 1}}\) on a level curved track of radius 5 \(m\). The coefficient of static friction between tyres and road is 0.1. Will the person slip while taking the turn with the same speed ? Take \(g = 10\,m{s^{ - 2}}\).
Choose the correct statement.

1 A person will slip if \({v^2} < 5{\mkern 1mu} {m^2}{s^{ - 2}}\)
2 A person will slip if \({v^2} = 5{\mkern 1mu} {m^2}{s^{ - 2}}\)
3 A person will not slip if \({v^2} > 10{\mkern 1mu} {m^2}{s^{ - 2}}\)
4 A person will slip if \({v^2} > 5{\mkern 1mu} {m^2}{s^{ - 2}}\)
PHXI05:LAWS OF MOTION

363218 A hemispherical bowl of radius \(R\) is rotated about its axis of symmetry which is kept vertical with angular velocity \(\omega \). A small block is kept in the bowl. It remains stationary relative to the bowl surface at a position where the radius makes an angle \(\theta \) with the vertical. The friction is absent. The value of \(\theta \) is :-

1 \({\cos ^{ - 1}}\left( {\frac{g}{{R{\omega ^2}}}} \right)\)
2 \({\sin ^{ - 1}}\left( {\frac{g}{{R{\omega ^2}}}} \right)\)
3 \({\tan ^{ - 1}}\left( {\frac{g}{{R{\omega ^2}}}} \right)\)
4 \({\rm{None }}\,{\rm{of }}\,{\rm{these}}\)
PHXI05:LAWS OF MOTION

363219 A block of mass \(m\) is projected on a smooth horizontal circular track with velocity \(v\). What is the average normal force exerted by the circular walls on the block during its motion from \(A\) to \(B\)?
supporting img

1 \(\frac{{m{v^2}}}{R}\)
2 \(\frac{{m{v^2}}}{{\pi R}}\)
3 \(\frac{{2\,m{v^2}}}{R}\)
4 \(\frac{{2m{v^2}}}{{\pi R}}\)
PHXI05:LAWS OF MOTION

363220 A circular race track of radius 300 \(m\) is banked at an angle of \({\rm{15}}^\circ \) . If the coefficient of friction between the wheels of a race car and the road is 0.2, what is the maximum permissible speed to avoid slipping? (Take \({\rm{tan15}}^\circ = 0.27\))

1 \(38.2\,m{s^{ - 1}}\)
2 \(48.2\,m{s^{ - 1}}\)
3 \(18.2\,m{s^{ - 1}}\)
4 \(28.2\,m{s^{ - 1}}\)
PHXI05:LAWS OF MOTION

363221 A small block of mass \(1\,kg\) is held by a light string rests on a smooth inclined plane which can turn about \({Z Z^{\prime}}\)-axis with an angular velocity \(2\,rad/s\) as shown in the figure. The block is at distance \({\dfrac{1}{\sqrt{2}} {~m}}\) from the point \({O}\). The tension in the string is \({(32)^{x} {~N}}\). Find the value of \({x}\) is
supporting img

1 2
2 5
3 4
4 1
PHXI05:LAWS OF MOTION

363222 A person is driving a vehicle at uniform speed of \(5\,m{s^{ - 1}}\) on a level curved track of radius 5 \(m\). The coefficient of static friction between tyres and road is 0.1. Will the person slip while taking the turn with the same speed ? Take \(g = 10\,m{s^{ - 2}}\).
Choose the correct statement.

1 A person will slip if \({v^2} < 5{\mkern 1mu} {m^2}{s^{ - 2}}\)
2 A person will slip if \({v^2} = 5{\mkern 1mu} {m^2}{s^{ - 2}}\)
3 A person will not slip if \({v^2} > 10{\mkern 1mu} {m^2}{s^{ - 2}}\)
4 A person will slip if \({v^2} > 5{\mkern 1mu} {m^2}{s^{ - 2}}\)