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

144052 A mass attached to one end of a string crosses top-most point on a vertical circle with critical speed. Its centripetal acceleration when string becomes horizontal will be ( \(\mathrm{g}=\) gravitational acceleration)

1 \(g\)
2 \(3 \mathrm{~g}\)
3 \(4 \mathrm{~g}\)
4 \(6 \mathrm{~g}\)
Motion in Plane

144053 A particle moves along a circle of radius ' \(r\) ' with constant tangential acceleration. If the velocity of the particle is ' \(v\) ' at the end of second revolution, after the revolution has started then the tangential acceleration is

1 \(\frac{v^{2}}{8 \pi r}\)
2 \(\frac{v^{2}}{6 \pi r}\)
3 \(\frac{\mathrm{v}^{2}}{4 \pi \mathrm{r}}\)
4 \(\frac{v^{2}}{2 \pi r}\)
Motion in Plane

144054 A particle of mass ' \(m\) ' is moving in circular path of constant radius ' \(r\) ' such that centripetal acceleration is varying with time ' \(t\) ' as \(K^{2} r t^{2}\) where \(K\) is a constant. The power delivered to the particle by the force acting on it is

1 \(\mathrm{m}^{2} \mathrm{~K}^{2} \mathrm{r}^{2} \mathrm{t}^{2}\)
2 \(\mathrm{m} \mathrm{K}^{2} \mathrm{r}^{2} \mathrm{t}\)
3 \(\mathrm{mK}^{2} \mathrm{rt}^{2}\)
4 \(\mathrm{mKr}^{2} \mathrm{t}\)
Motion in Plane

144056 An aeroplane executes a horizontal loop at a speed of \(720 \mathrm{~km} / \mathrm{h}\) with its wings banked at \(45^{\circ}\). What is the radius of the loop? Take \(\mathrm{g}=10 \mathrm{~ms}^{-2}\).

1 \(4 \mathrm{~km}\)
2 \(4.5 \mathrm{~km}\)
3 \(7.2 \mathrm{~km}\)
4 \(2 \mathrm{~km}\)
Motion in Plane

144058 A cyclist starts from the centre \(O\) of a circular park of radius one kilometre, reaches the edge \(P\) of the park, then cycles along the circumference and returns to the centre along QO as shown in the figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometre per hour) is :
original image

1 0,1
2 \(\frac{\pi+4}{2}, 0\)
3 \(21.4, \frac{\pi+4}{2}\)
4 \(0,21.4\)
Motion in Plane

144052 A mass attached to one end of a string crosses top-most point on a vertical circle with critical speed. Its centripetal acceleration when string becomes horizontal will be ( \(\mathrm{g}=\) gravitational acceleration)

1 \(g\)
2 \(3 \mathrm{~g}\)
3 \(4 \mathrm{~g}\)
4 \(6 \mathrm{~g}\)
Motion in Plane

144053 A particle moves along a circle of radius ' \(r\) ' with constant tangential acceleration. If the velocity of the particle is ' \(v\) ' at the end of second revolution, after the revolution has started then the tangential acceleration is

1 \(\frac{v^{2}}{8 \pi r}\)
2 \(\frac{v^{2}}{6 \pi r}\)
3 \(\frac{\mathrm{v}^{2}}{4 \pi \mathrm{r}}\)
4 \(\frac{v^{2}}{2 \pi r}\)
Motion in Plane

144054 A particle of mass ' \(m\) ' is moving in circular path of constant radius ' \(r\) ' such that centripetal acceleration is varying with time ' \(t\) ' as \(K^{2} r t^{2}\) where \(K\) is a constant. The power delivered to the particle by the force acting on it is

1 \(\mathrm{m}^{2} \mathrm{~K}^{2} \mathrm{r}^{2} \mathrm{t}^{2}\)
2 \(\mathrm{m} \mathrm{K}^{2} \mathrm{r}^{2} \mathrm{t}\)
3 \(\mathrm{mK}^{2} \mathrm{rt}^{2}\)
4 \(\mathrm{mKr}^{2} \mathrm{t}\)
Motion in Plane

144056 An aeroplane executes a horizontal loop at a speed of \(720 \mathrm{~km} / \mathrm{h}\) with its wings banked at \(45^{\circ}\). What is the radius of the loop? Take \(\mathrm{g}=10 \mathrm{~ms}^{-2}\).

1 \(4 \mathrm{~km}\)
2 \(4.5 \mathrm{~km}\)
3 \(7.2 \mathrm{~km}\)
4 \(2 \mathrm{~km}\)
Motion in Plane

144058 A cyclist starts from the centre \(O\) of a circular park of radius one kilometre, reaches the edge \(P\) of the park, then cycles along the circumference and returns to the centre along QO as shown in the figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometre per hour) is :
original image

1 0,1
2 \(\frac{\pi+4}{2}, 0\)
3 \(21.4, \frac{\pi+4}{2}\)
4 \(0,21.4\)
Motion in Plane

144052 A mass attached to one end of a string crosses top-most point on a vertical circle with critical speed. Its centripetal acceleration when string becomes horizontal will be ( \(\mathrm{g}=\) gravitational acceleration)

1 \(g\)
2 \(3 \mathrm{~g}\)
3 \(4 \mathrm{~g}\)
4 \(6 \mathrm{~g}\)
Motion in Plane

144053 A particle moves along a circle of radius ' \(r\) ' with constant tangential acceleration. If the velocity of the particle is ' \(v\) ' at the end of second revolution, after the revolution has started then the tangential acceleration is

1 \(\frac{v^{2}}{8 \pi r}\)
2 \(\frac{v^{2}}{6 \pi r}\)
3 \(\frac{\mathrm{v}^{2}}{4 \pi \mathrm{r}}\)
4 \(\frac{v^{2}}{2 \pi r}\)
Motion in Plane

144054 A particle of mass ' \(m\) ' is moving in circular path of constant radius ' \(r\) ' such that centripetal acceleration is varying with time ' \(t\) ' as \(K^{2} r t^{2}\) where \(K\) is a constant. The power delivered to the particle by the force acting on it is

1 \(\mathrm{m}^{2} \mathrm{~K}^{2} \mathrm{r}^{2} \mathrm{t}^{2}\)
2 \(\mathrm{m} \mathrm{K}^{2} \mathrm{r}^{2} \mathrm{t}\)
3 \(\mathrm{mK}^{2} \mathrm{rt}^{2}\)
4 \(\mathrm{mKr}^{2} \mathrm{t}\)
Motion in Plane

144056 An aeroplane executes a horizontal loop at a speed of \(720 \mathrm{~km} / \mathrm{h}\) with its wings banked at \(45^{\circ}\). What is the radius of the loop? Take \(\mathrm{g}=10 \mathrm{~ms}^{-2}\).

1 \(4 \mathrm{~km}\)
2 \(4.5 \mathrm{~km}\)
3 \(7.2 \mathrm{~km}\)
4 \(2 \mathrm{~km}\)
Motion in Plane

144058 A cyclist starts from the centre \(O\) of a circular park of radius one kilometre, reaches the edge \(P\) of the park, then cycles along the circumference and returns to the centre along QO as shown in the figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometre per hour) is :
original image

1 0,1
2 \(\frac{\pi+4}{2}, 0\)
3 \(21.4, \frac{\pi+4}{2}\)
4 \(0,21.4\)
Motion in Plane

144052 A mass attached to one end of a string crosses top-most point on a vertical circle with critical speed. Its centripetal acceleration when string becomes horizontal will be ( \(\mathrm{g}=\) gravitational acceleration)

1 \(g\)
2 \(3 \mathrm{~g}\)
3 \(4 \mathrm{~g}\)
4 \(6 \mathrm{~g}\)
Motion in Plane

144053 A particle moves along a circle of radius ' \(r\) ' with constant tangential acceleration. If the velocity of the particle is ' \(v\) ' at the end of second revolution, after the revolution has started then the tangential acceleration is

1 \(\frac{v^{2}}{8 \pi r}\)
2 \(\frac{v^{2}}{6 \pi r}\)
3 \(\frac{\mathrm{v}^{2}}{4 \pi \mathrm{r}}\)
4 \(\frac{v^{2}}{2 \pi r}\)
Motion in Plane

144054 A particle of mass ' \(m\) ' is moving in circular path of constant radius ' \(r\) ' such that centripetal acceleration is varying with time ' \(t\) ' as \(K^{2} r t^{2}\) where \(K\) is a constant. The power delivered to the particle by the force acting on it is

1 \(\mathrm{m}^{2} \mathrm{~K}^{2} \mathrm{r}^{2} \mathrm{t}^{2}\)
2 \(\mathrm{m} \mathrm{K}^{2} \mathrm{r}^{2} \mathrm{t}\)
3 \(\mathrm{mK}^{2} \mathrm{rt}^{2}\)
4 \(\mathrm{mKr}^{2} \mathrm{t}\)
Motion in Plane

144056 An aeroplane executes a horizontal loop at a speed of \(720 \mathrm{~km} / \mathrm{h}\) with its wings banked at \(45^{\circ}\). What is the radius of the loop? Take \(\mathrm{g}=10 \mathrm{~ms}^{-2}\).

1 \(4 \mathrm{~km}\)
2 \(4.5 \mathrm{~km}\)
3 \(7.2 \mathrm{~km}\)
4 \(2 \mathrm{~km}\)
Motion in Plane

144058 A cyclist starts from the centre \(O\) of a circular park of radius one kilometre, reaches the edge \(P\) of the park, then cycles along the circumference and returns to the centre along QO as shown in the figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometre per hour) is :
original image

1 0,1
2 \(\frac{\pi+4}{2}, 0\)
3 \(21.4, \frac{\pi+4}{2}\)
4 \(0,21.4\)
Motion in Plane

144052 A mass attached to one end of a string crosses top-most point on a vertical circle with critical speed. Its centripetal acceleration when string becomes horizontal will be ( \(\mathrm{g}=\) gravitational acceleration)

1 \(g\)
2 \(3 \mathrm{~g}\)
3 \(4 \mathrm{~g}\)
4 \(6 \mathrm{~g}\)
Motion in Plane

144053 A particle moves along a circle of radius ' \(r\) ' with constant tangential acceleration. If the velocity of the particle is ' \(v\) ' at the end of second revolution, after the revolution has started then the tangential acceleration is

1 \(\frac{v^{2}}{8 \pi r}\)
2 \(\frac{v^{2}}{6 \pi r}\)
3 \(\frac{\mathrm{v}^{2}}{4 \pi \mathrm{r}}\)
4 \(\frac{v^{2}}{2 \pi r}\)
Motion in Plane

144054 A particle of mass ' \(m\) ' is moving in circular path of constant radius ' \(r\) ' such that centripetal acceleration is varying with time ' \(t\) ' as \(K^{2} r t^{2}\) where \(K\) is a constant. The power delivered to the particle by the force acting on it is

1 \(\mathrm{m}^{2} \mathrm{~K}^{2} \mathrm{r}^{2} \mathrm{t}^{2}\)
2 \(\mathrm{m} \mathrm{K}^{2} \mathrm{r}^{2} \mathrm{t}\)
3 \(\mathrm{mK}^{2} \mathrm{rt}^{2}\)
4 \(\mathrm{mKr}^{2} \mathrm{t}\)
Motion in Plane

144056 An aeroplane executes a horizontal loop at a speed of \(720 \mathrm{~km} / \mathrm{h}\) with its wings banked at \(45^{\circ}\). What is the radius of the loop? Take \(\mathrm{g}=10 \mathrm{~ms}^{-2}\).

1 \(4 \mathrm{~km}\)
2 \(4.5 \mathrm{~km}\)
3 \(7.2 \mathrm{~km}\)
4 \(2 \mathrm{~km}\)
Motion in Plane

144058 A cyclist starts from the centre \(O\) of a circular park of radius one kilometre, reaches the edge \(P\) of the park, then cycles along the circumference and returns to the centre along QO as shown in the figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometre per hour) is :
original image

1 0,1
2 \(\frac{\pi+4}{2}, 0\)
3 \(21.4, \frac{\pi+4}{2}\)
4 \(0,21.4\)