Out of the following equations, which is the incorrect equation?

v → = r → x ω → \overrightarrow{v\ \ }=\overrightarrow{r\ }\ x\ \ \overrightarrow{\omega} v <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = r <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> x ω <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z">

τ → = r → x F → \ \overrightarrow{\tau\ }\ =\ \overrightarrow{r\ }\ x\ \overrightarrow{F} τ <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = r <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> x F <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z">

a R → = ω → x v → \overrightarrow{a_R}\ =\ \overrightarrow{\omega}\ x\ \overrightarrow{\ v}\ a R <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ω <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> x v <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z">

a T → = α → x r → \overrightarrow{a_T}\ =\ \overrightarrow{\alpha\ \ }\ x\ \ \overrightarrow{r\ } a T <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = α <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> x r <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z">

The formula for the period of the conical pendulum is ......

4 π l cos ⁡ θ 4 g 4\pi\sqrt{\frac{l\cos\theta}{4g}} 4 π 4 g l cos θ <path d="M473,2793c339.3,-1799.3,509.3,-2700,510,-2702 c3.3,-7.3,9.3,-11,18,-11H400000v40H1017.7s-90.5,478,-276.2,1466c-185.7,988, -279.5,1483,-281.5,1485c-2,6,-10,9,-24,9c-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32, -16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200c0,-1.3,-5.3,8.7,-16,30c-10.7, 21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26s76,-153,76,-153s77,-151, 77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,606z M1001 80H400000v40H1017z">

1 2 π l cos ⁡ θ g \frac{1}{2\pi}\sqrt{\frac{l\cos\theta}{g}} 2 π 1 g l cos θ <path d="M473,2793c339.3,-1799.3,509.3,-2700,510,-2702 c3.3,-7.3,9.3,-11,18,-11H400000v40H1017.7s-90.5,478,-276.2,1466c-185.7,988, -279.5,1483,-281.5,1485c-2,6,-10,9,-24,9c-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32, -16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200c0,-1.3,-5.3,8.7,-16,30c-10.7, 21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26s76,-153,76,-153s77,-151, 77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,606z M1001 80H400000v40H1017z">

1 2 π l sin ⁡ θ g \frac{1}{2\pi}\sqrt{\frac{l\sin\theta}{g}} 2 π 1 g l sin θ <path d="M473,2793c339.3,-1799.3,509.3,-2700,510,-2702 c3.3,-7.3,9.3,-11,18,-11H400000v40H1017.7s-90.5,478,-276.2,1466c-185.7,988, -279.5,1483,-281.5,1485c-2,6,-10,9,-24,9c-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32, -16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200c0,-1.3,-5.3,8.7,-16,30c-10.7, 21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26s76,-153,76,-153s77,-151, 77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,606z M1001 80H400000v40H1017z">

4 π l tan ⁡ θ g 4\pi\sqrt{\frac{l\tan\theta}{g}} 4 π g l tan θ <path d="M473,2793c339.3,-1799.3,509.3,-2700,510,-2702 c3.3,-7.3,9.3,-11,18,-11H400000v40H1017.7s-90.5,478,-276.2,1466c-185.7,988, -279.5,1483,-281.5,1485c-2,6,-10,9,-24,9c-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32, -16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200c0,-1.3,-5.3,8.7,-16,30c-10.7, 21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26s76,-153,76,-153s77,-151, 77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,606z M1001 80H400000v40H1017z">

A circular disc rotates about an axis passing through its centre with a certain angular velocity. Suddenly a small piece of the disc breaks from the edge and falls down. Then ........

its M.I. will decrease and the angular velocity will increase

its M.I. will increase and the angular velocity will decrease

both, the M.I. and the angular velocity will increase

both, the M.I. and the angular velocity will decrease

The moment of inertia of a body does not depend on ......

the angular velocity of the body

the axis of rotation of the body

the distribution of the mass of the body

The radius of gyration of a disc of radius R rotating about an axis perpendicular to its plane and tangential to the disc is .........

3 2 R \sqrt{\frac{3}{2}}\ R 2 3 <path d="M424,2478c-1.3,-0.7,-38.5,-172,-111.5,-514c-73, -342,-109.8,-513.3,-110.5,-514c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5, 25c-5.7,9.3,-9.8,16,-12.5,20s-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13, -13s76,-122,76,-122s77,-121,77,-121s209,968,209,968c0,-2,84.7,-361.7,254,-1079 c169.3,-717.3,254.7,-1077.7,256,-1081c4,-6.7,10,-10,18,-10H400000v40H1014.6 s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185c-2,6,-10,9,-24,9 c-8,0,-12,-0.7,-12,-2z M1001 80H400000v40H1014z"> R

R 2 \frac{R}{\sqrt{2}} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> R

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Practice Problem

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NGSS

HS-PS2-4, HS-PS2-1

Standards-aligned

SHARMISTHA DATTA

Used 159+ times

FREE Resource

20 questions

Show all answers

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The moments of inertia of two rotating bodies A and B about the same axis are I_A & I_B ( I_A > I_B ) and their angular momentum are equal. If K_A & K_Bare their rotational kinetic energies then......

K_A > K_B

K_A < K_B

K_A = K_B

K_A = K_B = 0

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A rigid body is rotating about an axis. to stop the rotation, we have to apply........

pressure

force

momentum

torque

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Two rings have their moments of inertia in the ratio 2 : 1 and their diameters are in the ratio 2 : 1. The ratio of their masses will be..........

2 : 1

1 : 2

1 : 4

1 : 1

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

A 2 kg mass is rotating on a circular path of radius 0.8 m with angular velocity of 44 rad/s. If the radius of the path becomes 1m, then the angular velocity will be ........

8.12 rad/s

19.28 rad/s

28.16 rad/s

35.26 rad/s

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

A disc of mass 2 kg and radius 20 cm is free rotate about an axis through its centre and perpendicular to the disc. If a force of 50 N is applied tangentially to the disc, then the angular acceleration is.......

250 rad/s²

25 rad/s²

2.5 rad/s²

0.25 rad/s²

For the uniform circular motion of a body, the direction of the centripetal force of a body.........

depends on the mass of the body

depends on the linear speed of the body

depends on the sense of rotation(clockwise or anticlockwise) of the body

does not depend on the sense of rotation(clockwise or anticlockwise) of the body

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

A car is moving on a banked track of radius 10m with a constant speed of 10 m/s. The angle of banking is ........
(g = 10 m/s²)

90⁰

60⁰

45⁰

30⁰

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The moments of inertia of two rotating bodies A and B about the same axis are I_A & I_B ( I_A > I_B ) and their angular momentum are equal. If K_A & K_Bare their rotational kinetic energies then......

A rigid body is rotating about an axis. to stop the rotation, we have to apply........

Two rings have their moments of inertia in the ratio 2 : 1 and their diameters are in the ratio 2 : 1. The ratio of their masses will be..........

A 2 kg mass is rotating on a circular path of radius 0.8 m with angular velocity of 44 rad/s. If the radius of the path becomes 1m, then the angular velocity will be ........

A disc of mass 2 kg and radius 20 cm is free rotate about an axis through its centre and perpendicular to the disc. If a force of 50 N is applied tangentially to the disc, then the angular acceleration is.......

For the uniform circular motion of a body, the direction of the centripetal force of a body.........

A car is moving on a banked track of radius 10m with a constant speed of 10 m/s. The angle of banking is ........
(g = 10 m/s²)

A cyclist moving at a speed of 20 m/s takes a turn. If he doubles his speed, then the chance of overturn........

A coin is placed on a disc rotating at a speed of 45 rpm. It flies away when the rotational speed of the disc becomes 50 rpm. If another identical coin is placed on the first coin , then both of them will fly away when the rotational speed is.......

A stone of mass 16 kg is attached to a string 144 m long and is whirled in a horizontal circle. The maximum tension the string can withstand is 16 N. Then the maximum speed that can be given to the stone without breaking the string is.........

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Rotational Dynamics

20 questions

The moments of inertia of two rotating bodies A and B about the same axis are IA & IB ( IA > IB ) and their angular momentum are equal. If KA & KB are their rotational kinetic energies then......

A rigid body is rotating about an axis. to stop the rotation, we have to apply........

Two rings have their moments of inertia in the ratio 2 : 1 and their diameters are in the ratio 2 : 1. The ratio of their masses will be..........

A 2 kg mass is rotating on a circular path of radius 0.8 m with angular velocity of 44 rad/s. If the radius of the path becomes 1m, then the angular velocity will be ........

A disc of mass 2 kg and radius 20 cm is free rotate about an axis through its centre and perpendicular to the disc. If a force of 50 N is applied tangentially to the disc, then the angular acceleration is.......

For the uniform circular motion of a body, the direction of the centripetal force of a body.........

A car is moving on a banked track of radius 10m with a constant speed of 10 m/s. The angle of banking is ........(g = 10 m/s2)

A cyclist moving at a speed of 20 m/s takes a turn. If he doubles his speed, then the chance of overturn........

A coin is placed on a disc rotating at a speed of 45 rpm. It flies away when the rotational speed of the disc becomes 50 rpm. If another identical coin is placed on the first coin , then both of them will fly away when the rotational speed is.......

A stone of mass 16 kg is attached to a string 144 m long and is whirled in a horizontal circle. The maximum tension the string can withstand is 16 N. Then the maximum speed that can be given to the stone without breaking the string is.........

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The moments of inertia of two rotating bodies A and B about the same axis are I_A & I_B ( I_A > I_B ) and their angular momentum are equal. If K_A & K_Bare their rotational kinetic energies then......

A car is moving on a banked track of radius 10m with a constant speed of 10 m/s. The angle of banking is ........
(g = 10 m/s²)