Tag: turning effects of forces

Questions Related to turning effects of forces

The centre of mass of a body:

physics turning effects of forces stability and centre of mass center of mass centre of mass

  1. Lies always at the geometrical center

  2. Lies always inside the body

  3. Lies always outside the body

  4. Lies within or outside the body

Show answer
Correct Option: D
Explanation:

The centre of mass of a body can lie within or outside the body.

For example, centre of mass of a uniform rod lies at its geometrical centre which lies within the rod whereas centre of mass of a uniform ring lies at its geometrical centre which lies outside the ring.

Two unequal masses are tied together with a cord with a compressed spring in between.
Which of the following energies is conserved for the system?

physics turning effects of forces stability and centre of mass center of mass centre of mass

  1. Kinetic energy

  2. Potential energy

  3. Mechanical energy

  4. None of these

Show answer
Correct Option: C
Explanation:
Both KE and PE are unserversed.
Hence, the answer is mechanical energy.


Two unequal masses are tied together with a cord with a compressed spring in between.
Which one is correct?

physics turning effects of forces stability and centre of mass center of mass centre of mass

  1. Both masses will have equal KE.

  2. Lighter block will have greater KE.

  3. Heavier block will have greater KE.

  4. None of above answers is correct.

Show answer
Correct Option: B
Explanation:
Lighter block will have greater kinetic energy to lighter block will have higher velocity mass so Heavier block, hence by equation $\dfrac{1}{2}mv^2,$ the lighter will have greater KE.
Hence, the answer is Lighter block will have greater KE.

A string is wrapped around a cylinder of mass $M$ and radius $R$. The string is pulled vertically upwards to prevent the centre of mass from falling as the cylinder unwinds the string, The work done on the cylinder for reaching an angular speed $\omega$ is:

physics turning effects of forces stability and centre of mass center of mass centre of mass

  1. $\cfrac { 2M{ R }^{ 2 }{ \omega }^{ 2 } }{ 3 } $

  2. $\cfrac { M{ R }^{ 2 }{ \omega }^{ 2 } }{ 3 } $

  3. $\cfrac { M{ R }^{ 2 }{ \omega }^{ 2 } }{ 2 } $

  4. $\cfrac { M{ R }^{ 2 }{ \omega }^{ 2 } }{ 4 } $

Show answer
Correct Option: D
Explanation:
Work done is the rotational KE acquired be cylinder,
$=\dfrac{1}{2} I\omega ^2$
$=\dfrac{1}{2}\dfrac{MR^2}{2}\omega ^2$
$=\dfrac{MR^2}{4}\omega ^2.$
Hence, the answer is $\dfrac{MR^2}{4}\omega ^2.$

A straight rod of length L has one of its ends at the origin and the other at $x=L$. If the mass per unit length of the rod is given by Ax where A is constant, where is its mass centre?

physics turning effects of forces stability and centre of mass center of mass centre of mass

  1. $L/3$

  2. $L/2$

  3. $2L/3$

  4. $3L/4$

Show answer
Correct Option: B
Explanation:
I assume you meant to say "a is a CONSTANT".

xc = coordinate of center of mass

M = total mass

$xc = ∫xdm / ∫dm = ∫xdm / M$

Given:$ m(x) = ax ⇒ dm/dx = a ⇒ dm = adx$

$∫xdm = ∫01 x(adx) = a/2$

$M = ∫dm = ∫(dm/dx)dx = ∫01 adx = a$

$xc = (a/2)/a = 1/2$

By the way, this is a mechanics problem (in statics), not a thermodynamics problem.

 

A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is $\alpha R$ fromthe centre of the bigger disc. The value of $\alpha$ is

physics turning effects of forces stability and centre of mass center of mass centre of mass

  1. $\cfrac{1}{2}$

  2. $\cfrac{1}{6}$

  3. $\cfrac{1}{4}$

  4. $\cfrac{1}{3}$

Show answer
Correct Option: D

State whether given statement is True or False.

Centre of gravity of a freely suspended body always lies vertically below the point of suspension.

physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Yes, Centre of gravity of a freely suspended body always lies vertically below the point of suspension. The center of gravity of an object is the point you can suspend the object from without there being any rotation because of the force of gravity, no matter how the object is oriented. If you suspend an object from any point, let it go and allow it to come to rest, the center of gravity will lie along a vertical line that passes through the point of suspension. Unless you've been exceedingly careful in balancing the object, the center of gravity will generally lie below the suspension point.

Where is the centre of gravity of a uniform ring situated ?

physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

  1. At the centre of ring.

  2. At the centre of semicircular ring

  3. At the centre of radius

  4. cant say

Show answer
Correct Option: A
Explanation:

Centre of gravity means a point from which the weight of a body or system may be considered to act. In uniform gravity it is the same as the centre of mass.For regular bodies centre of gravity lies at the centre of the body.Hence we know that there will be a centre for a uniform ring lamina.Hence this centre of the ring will be centre of gravity.

Stability and center of gravity of an object whose stability can be increased by

physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

  1. lowering center of gravity and increasing area of base

  2. lowering center of gravity and decreasing area of base

  3. moving center of gravity higher and increasing areas of base

  4. moving center of gravity higher and decreasing area of base

Show answer
Correct Option: A
Explanation:

The position of the centre of gravity of an object affects its stability. The lower the centre of gravity is, the more stable the object. The higher it is the more likely the object is to topple over if it is pushed.
In general, increasing the size of the base (that is area) of support increases stability.

Centre of gravity of the circular ring will be:
physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

  1. At the periphery

  2. At the center

  3. Outside it

  4. None

Show answer
Correct Option: B
Explanation:

Centre of gravity of the circle lies at its geometric centre because the resultant weight of the circle acts at its centre.