04. Circular Motion : Uniform Circular Motion, Dynamic Circular Motion
Motion in Plane

144072 If \(x=5 t+3 t^{2}\) and \(y=4 t\) are the \(x\) and \(y\) coordinates of a particle at any time \(t\) second where \(x\) and \(y\) are in metre, then the acceleration of the particle

1 Is zero throughout its motion
2 Is a constant throughout its motion
3 Depends only on its y component
4 Varies along both \(\mathrm{x}\) and \(\mathrm{y}\) direction
Motion in Plane

144073 Two particles are performing uniform circular motion about a centre of two concentric circles of radii ' \(r_{1}\) ', and ' \(r_{2}\) ', respectively. The two particles and the centre of circles lie on a straight line during the motion, then the ratio of their angular velocities will be

1 \(3: 1\)
2 \(2: 1\)
3 \(0.5: 1\)
4 \(1: 1\)
Motion in Plane

144075 A stone of mass \(3 \mathrm{~kg}\) attached at one end of a \(2 \mathrm{~m}\) long string is whirled in horizontal circle. The string makes an angle of \(45^{\circ}\) with the vertical then the centripetal force acting on the string is \(\left(g=10 \mathrm{~m} / \mathrm{s}^{2}, \tan 45^{\circ}=1\right)\)

1 \(20 \mathrm{~N}\)
2 \(30 \mathrm{~N}\)
3 \(10 \mathrm{~N}\)
4 \(40 \mathrm{~N}\)
Motion in Plane

144076 A body of mass ' \(m\) ' is moving along a circle of radius ' \(r\) ' with linear speed ' \(v\) '. Now, to change the linear speed to \(\frac{v}{2}\) and to move it along the circle of radius ' \(4 r^{\prime}\) ', required change in the centripetal force of the body is

1 decrease by \(\frac{15}{16}\)
2 decrease by \(\frac{5}{16}\)
3 increase by \(\frac{9}{16}\)
4 increase by \(\frac{11}{16}\)
Motion in Plane

144078 Mass of \(0.5 \mathrm{~kg}\) is attached to a string moving in horizontal circle with angular velocity 10 cycle/min. Keeping the radius constant, tension in the string is made 4 times by increasing angular velocity ' \(\omega\) '. The value ' \(\omega\) ' of that mass will be

1 \(\frac{1}{4}\) cycle \(/ \mathrm{s}\)
2 \(\frac{1}{2}\) cycle \(/ \mathrm{s}\)
3 \(\frac{1}{5}\) cycle \(/ \mathrm{s}\)
4 \(\frac{1}{3}\) cycle \(/ \mathrm{s}\)
Motion in Plane

144072 If \(x=5 t+3 t^{2}\) and \(y=4 t\) are the \(x\) and \(y\) coordinates of a particle at any time \(t\) second where \(x\) and \(y\) are in metre, then the acceleration of the particle

1 Is zero throughout its motion
2 Is a constant throughout its motion
3 Depends only on its y component
4 Varies along both \(\mathrm{x}\) and \(\mathrm{y}\) direction
Motion in Plane

144073 Two particles are performing uniform circular motion about a centre of two concentric circles of radii ' \(r_{1}\) ', and ' \(r_{2}\) ', respectively. The two particles and the centre of circles lie on a straight line during the motion, then the ratio of their angular velocities will be

1 \(3: 1\)
2 \(2: 1\)
3 \(0.5: 1\)
4 \(1: 1\)
Motion in Plane

144075 A stone of mass \(3 \mathrm{~kg}\) attached at one end of a \(2 \mathrm{~m}\) long string is whirled in horizontal circle. The string makes an angle of \(45^{\circ}\) with the vertical then the centripetal force acting on the string is \(\left(g=10 \mathrm{~m} / \mathrm{s}^{2}, \tan 45^{\circ}=1\right)\)

1 \(20 \mathrm{~N}\)
2 \(30 \mathrm{~N}\)
3 \(10 \mathrm{~N}\)
4 \(40 \mathrm{~N}\)
Motion in Plane

144076 A body of mass ' \(m\) ' is moving along a circle of radius ' \(r\) ' with linear speed ' \(v\) '. Now, to change the linear speed to \(\frac{v}{2}\) and to move it along the circle of radius ' \(4 r^{\prime}\) ', required change in the centripetal force of the body is

1 decrease by \(\frac{15}{16}\)
2 decrease by \(\frac{5}{16}\)
3 increase by \(\frac{9}{16}\)
4 increase by \(\frac{11}{16}\)
Motion in Plane

144078 Mass of \(0.5 \mathrm{~kg}\) is attached to a string moving in horizontal circle with angular velocity 10 cycle/min. Keeping the radius constant, tension in the string is made 4 times by increasing angular velocity ' \(\omega\) '. The value ' \(\omega\) ' of that mass will be

1 \(\frac{1}{4}\) cycle \(/ \mathrm{s}\)
2 \(\frac{1}{2}\) cycle \(/ \mathrm{s}\)
3 \(\frac{1}{5}\) cycle \(/ \mathrm{s}\)
4 \(\frac{1}{3}\) cycle \(/ \mathrm{s}\)
Motion in Plane

144072 If \(x=5 t+3 t^{2}\) and \(y=4 t\) are the \(x\) and \(y\) coordinates of a particle at any time \(t\) second where \(x\) and \(y\) are in metre, then the acceleration of the particle

1 Is zero throughout its motion
2 Is a constant throughout its motion
3 Depends only on its y component
4 Varies along both \(\mathrm{x}\) and \(\mathrm{y}\) direction
Motion in Plane

144073 Two particles are performing uniform circular motion about a centre of two concentric circles of radii ' \(r_{1}\) ', and ' \(r_{2}\) ', respectively. The two particles and the centre of circles lie on a straight line during the motion, then the ratio of their angular velocities will be

1 \(3: 1\)
2 \(2: 1\)
3 \(0.5: 1\)
4 \(1: 1\)
Motion in Plane

144075 A stone of mass \(3 \mathrm{~kg}\) attached at one end of a \(2 \mathrm{~m}\) long string is whirled in horizontal circle. The string makes an angle of \(45^{\circ}\) with the vertical then the centripetal force acting on the string is \(\left(g=10 \mathrm{~m} / \mathrm{s}^{2}, \tan 45^{\circ}=1\right)\)

1 \(20 \mathrm{~N}\)
2 \(30 \mathrm{~N}\)
3 \(10 \mathrm{~N}\)
4 \(40 \mathrm{~N}\)
Motion in Plane

144076 A body of mass ' \(m\) ' is moving along a circle of radius ' \(r\) ' with linear speed ' \(v\) '. Now, to change the linear speed to \(\frac{v}{2}\) and to move it along the circle of radius ' \(4 r^{\prime}\) ', required change in the centripetal force of the body is

1 decrease by \(\frac{15}{16}\)
2 decrease by \(\frac{5}{16}\)
3 increase by \(\frac{9}{16}\)
4 increase by \(\frac{11}{16}\)
Motion in Plane

144078 Mass of \(0.5 \mathrm{~kg}\) is attached to a string moving in horizontal circle with angular velocity 10 cycle/min. Keeping the radius constant, tension in the string is made 4 times by increasing angular velocity ' \(\omega\) '. The value ' \(\omega\) ' of that mass will be

1 \(\frac{1}{4}\) cycle \(/ \mathrm{s}\)
2 \(\frac{1}{2}\) cycle \(/ \mathrm{s}\)
3 \(\frac{1}{5}\) cycle \(/ \mathrm{s}\)
4 \(\frac{1}{3}\) cycle \(/ \mathrm{s}\)
Motion in Plane

144072 If \(x=5 t+3 t^{2}\) and \(y=4 t\) are the \(x\) and \(y\) coordinates of a particle at any time \(t\) second where \(x\) and \(y\) are in metre, then the acceleration of the particle

1 Is zero throughout its motion
2 Is a constant throughout its motion
3 Depends only on its y component
4 Varies along both \(\mathrm{x}\) and \(\mathrm{y}\) direction
Motion in Plane

144073 Two particles are performing uniform circular motion about a centre of two concentric circles of radii ' \(r_{1}\) ', and ' \(r_{2}\) ', respectively. The two particles and the centre of circles lie on a straight line during the motion, then the ratio of their angular velocities will be

1 \(3: 1\)
2 \(2: 1\)
3 \(0.5: 1\)
4 \(1: 1\)
Motion in Plane

144075 A stone of mass \(3 \mathrm{~kg}\) attached at one end of a \(2 \mathrm{~m}\) long string is whirled in horizontal circle. The string makes an angle of \(45^{\circ}\) with the vertical then the centripetal force acting on the string is \(\left(g=10 \mathrm{~m} / \mathrm{s}^{2}, \tan 45^{\circ}=1\right)\)

1 \(20 \mathrm{~N}\)
2 \(30 \mathrm{~N}\)
3 \(10 \mathrm{~N}\)
4 \(40 \mathrm{~N}\)
Motion in Plane

144076 A body of mass ' \(m\) ' is moving along a circle of radius ' \(r\) ' with linear speed ' \(v\) '. Now, to change the linear speed to \(\frac{v}{2}\) and to move it along the circle of radius ' \(4 r^{\prime}\) ', required change in the centripetal force of the body is

1 decrease by \(\frac{15}{16}\)
2 decrease by \(\frac{5}{16}\)
3 increase by \(\frac{9}{16}\)
4 increase by \(\frac{11}{16}\)
Motion in Plane

144078 Mass of \(0.5 \mathrm{~kg}\) is attached to a string moving in horizontal circle with angular velocity 10 cycle/min. Keeping the radius constant, tension in the string is made 4 times by increasing angular velocity ' \(\omega\) '. The value ' \(\omega\) ' of that mass will be

1 \(\frac{1}{4}\) cycle \(/ \mathrm{s}\)
2 \(\frac{1}{2}\) cycle \(/ \mathrm{s}\)
3 \(\frac{1}{5}\) cycle \(/ \mathrm{s}\)
4 \(\frac{1}{3}\) cycle \(/ \mathrm{s}\)
Motion in Plane

144072 If \(x=5 t+3 t^{2}\) and \(y=4 t\) are the \(x\) and \(y\) coordinates of a particle at any time \(t\) second where \(x\) and \(y\) are in metre, then the acceleration of the particle

1 Is zero throughout its motion
2 Is a constant throughout its motion
3 Depends only on its y component
4 Varies along both \(\mathrm{x}\) and \(\mathrm{y}\) direction
Motion in Plane

144073 Two particles are performing uniform circular motion about a centre of two concentric circles of radii ' \(r_{1}\) ', and ' \(r_{2}\) ', respectively. The two particles and the centre of circles lie on a straight line during the motion, then the ratio of their angular velocities will be

1 \(3: 1\)
2 \(2: 1\)
3 \(0.5: 1\)
4 \(1: 1\)
Motion in Plane

144075 A stone of mass \(3 \mathrm{~kg}\) attached at one end of a \(2 \mathrm{~m}\) long string is whirled in horizontal circle. The string makes an angle of \(45^{\circ}\) with the vertical then the centripetal force acting on the string is \(\left(g=10 \mathrm{~m} / \mathrm{s}^{2}, \tan 45^{\circ}=1\right)\)

1 \(20 \mathrm{~N}\)
2 \(30 \mathrm{~N}\)
3 \(10 \mathrm{~N}\)
4 \(40 \mathrm{~N}\)
Motion in Plane

144076 A body of mass ' \(m\) ' is moving along a circle of radius ' \(r\) ' with linear speed ' \(v\) '. Now, to change the linear speed to \(\frac{v}{2}\) and to move it along the circle of radius ' \(4 r^{\prime}\) ', required change in the centripetal force of the body is

1 decrease by \(\frac{15}{16}\)
2 decrease by \(\frac{5}{16}\)
3 increase by \(\frac{9}{16}\)
4 increase by \(\frac{11}{16}\)
Motion in Plane

144078 Mass of \(0.5 \mathrm{~kg}\) is attached to a string moving in horizontal circle with angular velocity 10 cycle/min. Keeping the radius constant, tension in the string is made 4 times by increasing angular velocity ' \(\omega\) '. The value ' \(\omega\) ' of that mass will be

1 \(\frac{1}{4}\) cycle \(/ \mathrm{s}\)
2 \(\frac{1}{2}\) cycle \(/ \mathrm{s}\)
3 \(\frac{1}{5}\) cycle \(/ \mathrm{s}\)
4 \(\frac{1}{3}\) cycle \(/ \mathrm{s}\)