Tag: couple

Questions Related to couple

A uniform meter rule is pivoted at its mid-point. A weight of $50gf$ suspended at one end of it. Where should a weight of $100 gf$ be suspended to keep the rule horizontal : 

physics turning on a pivot the turning effect of a force moment of force or torque turning effect of force couple

  1. At distance $50  \ cm$ from the pivoted end.

  2. At distance $12.5 \ cm$ from the other end.

  3. At distance $37.5 \  cm$ from the other end.

  4. At distance $25 \ cm$ from the pivoted end.

Show answer
Correct Option: D
Explanation:

As we have one meter rule pivoted at midpoint there will be a perpendicular distance of 50 cm from the contact of force of 50gf.
 Here we have moment of force of $r \times F$.
After substituting we get $moment\ of\ force = 50\times50 gf cm$.
Here this must be balanced by 100gf's moment of force.
 Let us think that there would be x perpendicular distance.
On equating we get 
$ 50\times50  gf cm = 100\times x gf cm$
$ x = 50\times 50/100 = 25 cm$. 

Hence $100 gf$ must be applied at a distance of $25 cm $.

A body is acted upon by two forces each of magnitude $F$, but in opposite directions. State the effect of the forces if both forces act at the same point of the body. Which of the following is/are true?

physics turning on a pivot the turning effect of a force moment of force or torque turning effect of force couple

  1. Resultant force $=0$

  2. Moment of forces $=0$

  3. No motion

  4. All of the above

Show answer
Correct Option: D
Explanation:

Here, we are applying two force in same magnitude but in opposite that is one is F and -F. Hence resultant force is $F + (-F) = 0 $. 

Hence, resultant force is zero. Here perpendicular distance is same for both the forces.
Hence, if we calculate $r \times F$ cross product. We get the same magnitude of moments but opposite in direction as force are of opposite in direction. Hence moments are also zeroes. Without any resultant and moment there will be no motion.

Name the factor on which moment of inertia of a body depends .

physics turning on a pivot the turning effect of a force moment of force or torque turning effect of force couple

  1. Mass

  2. Force

  3. Distance from rotating axis.

  4. Density

Show answer
Correct Option: A,C
Explanation:

Moment of inertia of a body depends  on the body's mass distribution and the axis of rotation.
The moment of inertia of a body is directly proportional to its mass and increases as the mass is moved further from the axis of rotation.
Answer (A) Mass & (C) Distance from rotating axis.

A uniform metre rule of mass $100g$ is balanced on a fulcrum at mark $40cm$ by suspending an unknown mass $m$ at the mark $20cm$ . To which side the rule will tilt if the mass $m$ is moved to the mark $10cm$?

physics turning on a pivot the turning effect of a force moment of force or torque turning effect of force couple

  1. on the side of mass $m$

  2. on the other side of mass $m$

  3. can't say

  4. it won't tilt

Show answer
Correct Option: A
Explanation:

As 100 g is balanced at fulcrum it will have a perpendicular distance of 40 cm from itself and mass m will have $100 - 20 = 80 cm $.


Here moment of forces are equal that is balance each other.Hence $ m\times 80 = 100\times  40 \Rightarrow $

$ m = 100/2 = 50 g $.

If there is mark at 10 cm then perpendicular distance would be 90 cm and moment of force would be $50\times90 = 4500\times g \ dyne - cm$ 
where as first moment of force is $100\times40 = 400\times g\ dyne- cm $. 

Hence it tilts on mass m side as it has more moment of force.

Which of the following playground equipment make use of the turning effect of forces?

physics turning on a pivot the turning effect of a force moment of force or torque turning effect of force couple

  1. See-saw

  2. Slide

  3. Swing

  4. Sand-box

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Correct Option: A,C
Explanation:

The forces acting on the see-saw and swing produces torque and make them to rotate. See-saw and Swing make use of the effect of forces.

A small piece of space junk is at rest in outer space. A very small asteroid strikes it, exerting a force on it that is NOT directed through the piece of space junk's center of mass.
Which of the following describes the motion of the piece of space junk DURING the asteroid strike?

physics turning on a pivot the turning effect of a force moment of force or torque turning effect of force couple

  1. Because the asteroid is small, the space junk remains at rest

  2. The piece of space junk spins, but does NOT move linearly

  3. The piece of space junk moves at constant velocity linearly, but does NOT spin

  4. The piece of space junk accelerates linearly, but does NOT spin

  5. The piece of space junk accelerates linearly, AND spins

Show answer
Correct Option: A
Explanation:

Due to striking the space junk, the asteroid will exert a force on the junk piece.

This force is not directed towards the of mass of the junk.
Hence the junk would experience a linear acceleration given by $a=\dfrac{F}{m}$
And also the angular acceleration as provided by the force=$\dfrac{Fl}{I}$
where $l$ is the least distance between the center of mass of junk and line along which asteroid moves,
and $I $ is the moment of inertia of the space junk.

A body is under the action of two equal and oppositely directed forces and the body is rotating with constant non-zero angular acceleration. Which of the following cannot be the separation between the lines of action of the forces?

physics turning on a pivot the turning effect of a force moment of force or torque turning effect of force couple

  1. $1m$

  2. $0.4m$

  3. $0.25m$

  4. zero

Show answer
Correct Option: D
Explanation:

A pair of equal and opposite forces acting on a body is called a couple.

It only gives a rotating effect to the body and the torque due to a couple is
given by $\tau = Fd$
where $F$ is equal to the  magnitude of one of the forces and 
$d$ is the distance between their points of application.
To produce a non-zero angular acceleration , the torque on the body must be non zero.
Hence , the couple can give a non-zero angular acceleration to the body
only when the distance between the points of applications of the forces is non-zero.   

Two small kids weighing 10 kg and 15 kg are trying to balance a seesaw of total length 5m, with the fulcrum at the centre. If one of the kids is sitting at an end, where should the other sit?

physics force the turning of couple couple turning effect of force

  1. $2.5 m$

  2. $1 m$

  3. $1.7 m$

  4. $2 m$

Show answer
Correct Option: C

 If principle of moments for any object holds, then object is in state of

physics turning on a pivot the turning of couple couple turning effect of force the turning effect of a force moment of force or torque

  1. inertia

  2. equilibrium

  3. suspension

  4. motion

Show answer
Correct Option: B
Explanation:

If principle of moments hold good, then the net torque about a given point is zero (usually CM or the pivoted point is zero). Hence the object does not rotate and is said to be in equilibrium

A uniform dice of mass $10kg$ radius $1m$ is placed on a rought horizontal surface. The coefficient of friction between the disc and the surface is $0.2$. A horizontal time varying force is applied on the centre of the disc whose variation with time is shown in graph.
List-I                                                         List-IIDisc rolls without slipping                   at $t=7s$Disc rolls with slipping                       at $t=3s$  Disc starts slipping at                         at $t=4s$Friction force is $10N$ at              None

physics turning on a pivot the turning of couple couple turning effect of force the turning effect of a force moment of force or torque

  1. $A-p,q;B-p;C-r;Dq$

  2. $A-p,r;B-s;C-s,p;D-q$

  3. $A-q,r;B-p;C-s;D-q$

  4. $A-p,q,r;B-q;r;C-s;p;D-p,q,r,s$

Show answer
Correct Option: C