Circular Motion
PHXI05:LAWS OF MOTION

363188 A particle is projected horizontally with a speed \({15 {~m} {~s}^{-1}}\) at a height 200 \(m\) above the ground at time \({t=0}\). What is the tangential acceleration of the particle at time \({t=2 {sec}}\) ? Assume \({g=10 {~m} {~s}^{2}}\).

1 \({6 {~m} {~s}^{-2}}\)
2 \({8 {~m} {~s}^{-2}}\)
3 \({10 {~m} {~s}^{-2}}\)
4 \({12 {~m} {~s}^{-2}}\)
PHXI05:LAWS OF MOTION

363189 A child starts running from rest along a circular track of radius \(r\) with constant tangential acceleration \(a\). After time \(t\) he feels that slipping of shoes on the ground has started. The coefficient of friction between shoes and the ground is[ \(g\) \(=\) acceleration due to gravity]

1 \(\frac{{{{\left[ {{a^4}{t^4} + {a^2}{r^2}} \right]}^{\frac{1}{2}}}}}{{gr}}\)
2 \(\frac{{\left[ {{a^4}{t^4} + {a^2}{r^2}} \right]}}{{rg}}\)
3 \(\frac{{\left[ {{a^2}{t^2} + {a^4}{r^4}} \right]}}{{rg}}\)
4 \(\frac{{{{\left[ {{a^4}{t^4} - {a^2}{r^2}} \right]}^{\frac{1}{2}}}}}{{rg}}\)
PHXI05:LAWS OF MOTION

363190 A car starts from rest and starts moving on a circular path of radius 100 \(m\) such that its speed increases at the rate of \({5 {~m} {~s}^{-2}}\). What is the radial acceleration of the car at the instant it makes one complete round trip (in \({{m} {s}^{-2}}\) )?

1 \(20\,\pi \)
2 \(10\,\pi \)
3 \(40\,\pi \)
4 \(30\,\pi \)
PHXI05:LAWS OF MOTION

363191 A circular race track of radius 300 \(m\) is banked at an angle of \(15^\circ \) . 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 \(\tan 15^\circ = 0.27\) )

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

363192 A car starts from rest with a constant tangential acceleration \({a_{0}}\) in a circular path of radius \({r}\). At time \({t_{0}}\) the car skids, find the value of coefficient of friction.

1 \({\dfrac{a_{0}}{g}}\)
2 \({\dfrac{a_{0}}{g} \sqrt{1+\dfrac{a_{0}^{2} t_{0}^{2}}{2 r}}}\)
3 \({\dfrac{a_{0}}{g} \sqrt{1+\dfrac{a_{0}^{2} t_{0}^{4}}{r^{2}}}}\)
4 \({\dfrac{a_{0}}{4 g}}\)
PHXI05:LAWS OF MOTION

363188 A particle is projected horizontally with a speed \({15 {~m} {~s}^{-1}}\) at a height 200 \(m\) above the ground at time \({t=0}\). What is the tangential acceleration of the particle at time \({t=2 {sec}}\) ? Assume \({g=10 {~m} {~s}^{2}}\).

1 \({6 {~m} {~s}^{-2}}\)
2 \({8 {~m} {~s}^{-2}}\)
3 \({10 {~m} {~s}^{-2}}\)
4 \({12 {~m} {~s}^{-2}}\)
PHXI05:LAWS OF MOTION

363189 A child starts running from rest along a circular track of radius \(r\) with constant tangential acceleration \(a\). After time \(t\) he feels that slipping of shoes on the ground has started. The coefficient of friction between shoes and the ground is[ \(g\) \(=\) acceleration due to gravity]

1 \(\frac{{{{\left[ {{a^4}{t^4} + {a^2}{r^2}} \right]}^{\frac{1}{2}}}}}{{gr}}\)
2 \(\frac{{\left[ {{a^4}{t^4} + {a^2}{r^2}} \right]}}{{rg}}\)
3 \(\frac{{\left[ {{a^2}{t^2} + {a^4}{r^4}} \right]}}{{rg}}\)
4 \(\frac{{{{\left[ {{a^4}{t^4} - {a^2}{r^2}} \right]}^{\frac{1}{2}}}}}{{rg}}\)
PHXI05:LAWS OF MOTION

363190 A car starts from rest and starts moving on a circular path of radius 100 \(m\) such that its speed increases at the rate of \({5 {~m} {~s}^{-2}}\). What is the radial acceleration of the car at the instant it makes one complete round trip (in \({{m} {s}^{-2}}\) )?

1 \(20\,\pi \)
2 \(10\,\pi \)
3 \(40\,\pi \)
4 \(30\,\pi \)
PHXI05:LAWS OF MOTION

363191 A circular race track of radius 300 \(m\) is banked at an angle of \(15^\circ \) . 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 \(\tan 15^\circ = 0.27\) )

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

363192 A car starts from rest with a constant tangential acceleration \({a_{0}}\) in a circular path of radius \({r}\). At time \({t_{0}}\) the car skids, find the value of coefficient of friction.

1 \({\dfrac{a_{0}}{g}}\)
2 \({\dfrac{a_{0}}{g} \sqrt{1+\dfrac{a_{0}^{2} t_{0}^{2}}{2 r}}}\)
3 \({\dfrac{a_{0}}{g} \sqrt{1+\dfrac{a_{0}^{2} t_{0}^{4}}{r^{2}}}}\)
4 \({\dfrac{a_{0}}{4 g}}\)
PHXI05:LAWS OF MOTION

363188 A particle is projected horizontally with a speed \({15 {~m} {~s}^{-1}}\) at a height 200 \(m\) above the ground at time \({t=0}\). What is the tangential acceleration of the particle at time \({t=2 {sec}}\) ? Assume \({g=10 {~m} {~s}^{2}}\).

1 \({6 {~m} {~s}^{-2}}\)
2 \({8 {~m} {~s}^{-2}}\)
3 \({10 {~m} {~s}^{-2}}\)
4 \({12 {~m} {~s}^{-2}}\)
PHXI05:LAWS OF MOTION

363189 A child starts running from rest along a circular track of radius \(r\) with constant tangential acceleration \(a\). After time \(t\) he feels that slipping of shoes on the ground has started. The coefficient of friction between shoes and the ground is[ \(g\) \(=\) acceleration due to gravity]

1 \(\frac{{{{\left[ {{a^4}{t^4} + {a^2}{r^2}} \right]}^{\frac{1}{2}}}}}{{gr}}\)
2 \(\frac{{\left[ {{a^4}{t^4} + {a^2}{r^2}} \right]}}{{rg}}\)
3 \(\frac{{\left[ {{a^2}{t^2} + {a^4}{r^4}} \right]}}{{rg}}\)
4 \(\frac{{{{\left[ {{a^4}{t^4} - {a^2}{r^2}} \right]}^{\frac{1}{2}}}}}{{rg}}\)
PHXI05:LAWS OF MOTION

363190 A car starts from rest and starts moving on a circular path of radius 100 \(m\) such that its speed increases at the rate of \({5 {~m} {~s}^{-2}}\). What is the radial acceleration of the car at the instant it makes one complete round trip (in \({{m} {s}^{-2}}\) )?

1 \(20\,\pi \)
2 \(10\,\pi \)
3 \(40\,\pi \)
4 \(30\,\pi \)
PHXI05:LAWS OF MOTION

363191 A circular race track of radius 300 \(m\) is banked at an angle of \(15^\circ \) . 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 \(\tan 15^\circ = 0.27\) )

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

363192 A car starts from rest with a constant tangential acceleration \({a_{0}}\) in a circular path of radius \({r}\). At time \({t_{0}}\) the car skids, find the value of coefficient of friction.

1 \({\dfrac{a_{0}}{g}}\)
2 \({\dfrac{a_{0}}{g} \sqrt{1+\dfrac{a_{0}^{2} t_{0}^{2}}{2 r}}}\)
3 \({\dfrac{a_{0}}{g} \sqrt{1+\dfrac{a_{0}^{2} t_{0}^{4}}{r^{2}}}}\)
4 \({\dfrac{a_{0}}{4 g}}\)
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PHXI05:LAWS OF MOTION

363188 A particle is projected horizontally with a speed \({15 {~m} {~s}^{-1}}\) at a height 200 \(m\) above the ground at time \({t=0}\). What is the tangential acceleration of the particle at time \({t=2 {sec}}\) ? Assume \({g=10 {~m} {~s}^{2}}\).

1 \({6 {~m} {~s}^{-2}}\)
2 \({8 {~m} {~s}^{-2}}\)
3 \({10 {~m} {~s}^{-2}}\)
4 \({12 {~m} {~s}^{-2}}\)
PHXI05:LAWS OF MOTION

363189 A child starts running from rest along a circular track of radius \(r\) with constant tangential acceleration \(a\). After time \(t\) he feels that slipping of shoes on the ground has started. The coefficient of friction between shoes and the ground is[ \(g\) \(=\) acceleration due to gravity]

1 \(\frac{{{{\left[ {{a^4}{t^4} + {a^2}{r^2}} \right]}^{\frac{1}{2}}}}}{{gr}}\)
2 \(\frac{{\left[ {{a^4}{t^4} + {a^2}{r^2}} \right]}}{{rg}}\)
3 \(\frac{{\left[ {{a^2}{t^2} + {a^4}{r^4}} \right]}}{{rg}}\)
4 \(\frac{{{{\left[ {{a^4}{t^4} - {a^2}{r^2}} \right]}^{\frac{1}{2}}}}}{{rg}}\)
PHXI05:LAWS OF MOTION

363190 A car starts from rest and starts moving on a circular path of radius 100 \(m\) such that its speed increases at the rate of \({5 {~m} {~s}^{-2}}\). What is the radial acceleration of the car at the instant it makes one complete round trip (in \({{m} {s}^{-2}}\) )?

1 \(20\,\pi \)
2 \(10\,\pi \)
3 \(40\,\pi \)
4 \(30\,\pi \)
PHXI05:LAWS OF MOTION

363191 A circular race track of radius 300 \(m\) is banked at an angle of \(15^\circ \) . 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 \(\tan 15^\circ = 0.27\) )

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

363192 A car starts from rest with a constant tangential acceleration \({a_{0}}\) in a circular path of radius \({r}\). At time \({t_{0}}\) the car skids, find the value of coefficient of friction.

1 \({\dfrac{a_{0}}{g}}\)
2 \({\dfrac{a_{0}}{g} \sqrt{1+\dfrac{a_{0}^{2} t_{0}^{2}}{2 r}}}\)
3 \({\dfrac{a_{0}}{g} \sqrt{1+\dfrac{a_{0}^{2} t_{0}^{4}}{r^{2}}}}\)
4 \({\dfrac{a_{0}}{4 g}}\)
PHXI05:LAWS OF MOTION

363188 A particle is projected horizontally with a speed \({15 {~m} {~s}^{-1}}\) at a height 200 \(m\) above the ground at time \({t=0}\). What is the tangential acceleration of the particle at time \({t=2 {sec}}\) ? Assume \({g=10 {~m} {~s}^{2}}\).

1 \({6 {~m} {~s}^{-2}}\)
2 \({8 {~m} {~s}^{-2}}\)
3 \({10 {~m} {~s}^{-2}}\)
4 \({12 {~m} {~s}^{-2}}\)
PHXI05:LAWS OF MOTION

363189 A child starts running from rest along a circular track of radius \(r\) with constant tangential acceleration \(a\). After time \(t\) he feels that slipping of shoes on the ground has started. The coefficient of friction between shoes and the ground is[ \(g\) \(=\) acceleration due to gravity]

1 \(\frac{{{{\left[ {{a^4}{t^4} + {a^2}{r^2}} \right]}^{\frac{1}{2}}}}}{{gr}}\)
2 \(\frac{{\left[ {{a^4}{t^4} + {a^2}{r^2}} \right]}}{{rg}}\)
3 \(\frac{{\left[ {{a^2}{t^2} + {a^4}{r^4}} \right]}}{{rg}}\)
4 \(\frac{{{{\left[ {{a^4}{t^4} - {a^2}{r^2}} \right]}^{\frac{1}{2}}}}}{{rg}}\)
PHXI05:LAWS OF MOTION

363190 A car starts from rest and starts moving on a circular path of radius 100 \(m\) such that its speed increases at the rate of \({5 {~m} {~s}^{-2}}\). What is the radial acceleration of the car at the instant it makes one complete round trip (in \({{m} {s}^{-2}}\) )?

1 \(20\,\pi \)
2 \(10\,\pi \)
3 \(40\,\pi \)
4 \(30\,\pi \)
PHXI05:LAWS OF MOTION

363191 A circular race track of radius 300 \(m\) is banked at an angle of \(15^\circ \) . 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 \(\tan 15^\circ = 0.27\) )

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

363192 A car starts from rest with a constant tangential acceleration \({a_{0}}\) in a circular path of radius \({r}\). At time \({t_{0}}\) the car skids, find the value of coefficient of friction.

1 \({\dfrac{a_{0}}{g}}\)
2 \({\dfrac{a_{0}}{g} \sqrt{1+\dfrac{a_{0}^{2} t_{0}^{2}}{2 r}}}\)
3 \({\dfrac{a_{0}}{g} \sqrt{1+\dfrac{a_{0}^{2} t_{0}^{4}}{r^{2}}}}\)
4 \({\dfrac{a_{0}}{4 g}}\)