A force F → = ( i ^ - 2 j ^ + 5 k ^ ) N is acting at a point r → = ( 2 i ^ + j ^ + 3 k ^ ) m . Find torque about the origin.

Given force acting on a point is F → = ( i ^ - 2 j ^ + 5 k ^ ) N , And, position vector of the point is r → = ( 2 i ^ + j ^ + 3 k ^ ) m We know that the torque is given as; τ → = r → × F → ⇒ r → × F → = i ^ j ^ k ^ 2 1 3 1 - 2 5 = i ^ [ ( 1 × 5 ) - ( - 2 × 3 ) ] - j ^ [ ( 2 × 5 ) - ( 1 × 3 ) ] + k ^ [ ( 2 × - 2 ) - ( 1 × 1 ) ] = ( 11 i ^ - 7 j ^ - 5 k ^ ) N m . Hence, the required torque is τ → = ( 11 i ^ - 7 j ^ - 5 k ^ ) N m .

A force F → = ( i ^ - 2 j ^ + 5 k ^ ) N is acting at a point r → = ( 2 i ^ + j ^ + 3 k ^ ) m . Find torque about the origin.

Given force acting on a point is F → = ( i ^ - 2 j ^ + 5 k ^ ) N , And, position vector of the point is r → = ( 2 i ^ + j ^ + 3 k ^ ) m We know that the torque is given as; τ → = r → × F → ⇒ r → × F → = i ^ j ^ k ^ 2 1 3 1 - 2 5 = i ^ [ ( 1 × 5 ) - ( - 2 × 3 ) ] - j ^ [ ( 2 × 5 ) - ( 1 × 3 ) ] + k ^ [ ( 2 × - 2 ) - ( 1 × 1 ) ] = ( 11 i ^ - 7 j ^ - 5 k ^ ) N m . Hence, the required torque is τ → = ( 11 i ^ - 7 j ^ - 5 k ^ ) N m .

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A force $\vec{F} = (\hat{i} - 2 \hat{j} + 5 \hat{k}) N$ is acting at a point $\vec{r} = (2 \hat{i} + \hat{j} + 3 \hat{k}) m$ . Find torque about the origin.

Important Questions on Rotational Mechanics

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Beta Question Bank for Medical: Physics>Chapter 10 - Rotational Mechanics>BEGINNER'S BOX - 3>Q 4

The density of a rod

A B

increases continuously from

A

B

. Is it easier to set it in rotation by clamping it at

A

and applying a perpendicular force at

B

or by clamping it at

B

and applying the force at

A

? Explain your answer.

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Beta Question Bank for Medical: Physics>Chapter 10 - Rotational Mechanics>BEGINNER'S BOX - 3>Q 5

A uniform disc of radius

20 cm

and mass

2 kg

can rotate about a fixed axis through the centre and perpendicular to its plane. A massless cord is round along the rim of the disc. If a uniform force of

2 newtons

is applied on the cord, tangential acceleration of a point on the rim of the disc will be

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Beta Question Bank for Medical: Physics>Chapter 10 - Rotational Mechanics>BEGINNER'S BOX - 3>Q 6

A door

1.6 m

wide requires a minimum force of

1 N

to be applied at the free end to open or close it. The minimum force that is required at a point

0.4 m

away from the hinges for opening or closing the door is

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Beta Question Bank for Medical: Physics>Chapter 10 - Rotational Mechanics>BEGINNER'S BOX - 3>Q 7

Four equal and parallel forces are acting on a rod (as shown in figure at distances of $20 cm$ , $40 cm$ , $60 cm$ and $80 cm$ respectively from one end of the rod. Under the influence of these forces the rod
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Beta Question Bank for Medical: Physics>Chapter 10 - Rotational Mechanics>BEGINNER'S BOX - 3>Q 8

A weightless rod is acted on by upward parallel forces of

2 N

and

4 N

at ends

A

and

B

, respectively. The total length of the rod is

AB = 3 m

. To keep the rod in equilibrium, a force of

6 N

should act in the following manner:

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Beta Question Bank for Medical: Physics>Chapter 10 - Rotational Mechanics>BEGINNER'S BOX - 4>Q 1

The figure shows a uniform disc, with mass $M = 2.4 kg$ and radius $R = 20 cm$ , mounted on a fixed horizontal axle. A block of mass $m = 1.2 kg$ hangs from a massless cord that is wrapped around the rim of the disc. The tension in the cord is:

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Beta Question Bank for Medical: Physics>Chapter 10 - Rotational Mechanics>BEGINNER'S BOX - 4>Q 2

A thin uniform stick of length $l$ and mass $m$ is held horizontally with its end $B$ hinged on the edge of a table. The point $A$ is suddenly released. The acceleration of the centre of mass of the stick at the time of release is:

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Beta Question Bank for Medical: Physics>Chapter 10 - Rotational Mechanics>BEGINNER'S BOX - 4>Q 3

If the earth is a point mass of

6 \times 10^{24} kg

revolving around the sun at a distance of

1.5 \times 10^{8} km

and in time, of

T = 3.14 \times 10^{7} seconds

, then the angular momentum of the earth around the sun is:

A force F→=(i^-2j^+5k^) N is acting at a point r→=(2i^+j^+3k^) m. Find torque about the origin.

Important Questions on Rotational Mechanics

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A force $\vec{F} = (\hat{i} - 2 \hat{j} + 5 \hat{k}) N$ is acting at a point $\vec{r} = (2 \hat{i} + \hat{j} + 3 \hat{k}) m$ . Find torque about the origin.