Tag: centre of mass

Quizzes (1) Questions (44)

Questions Related to centre of mass

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

Location of centre of mass of uniform semi-circular plate of radius R from its centre is:

  1. $\dfrac{2R}{3\pi}$

  2. $\dfrac{R}{3\pi}$

  3. $\dfrac{3R}{4\pi}$

  4. $\dfrac{4R}{3\pi}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The center of mass of a uniform semi-circular plate of radius R is located on the axis of symmetry at a distance of 4R / (3 * pi) from the center of the base.

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

Four bodies of masses 1,2,3,4 kg respectively are placed at the corners of a square of side $'a'$. Coordinates of centre of mass are (take $1\ kg$ at origin, $2\ kg$ on X-axis and $4\ kg$ on Y-axis)

  1. $\Big \lgroup \dfrac{7a}{10}, \dfrac{a}{2} \Big \rgroup$

  2. $\Big \lgroup \dfrac{a}{2}, \dfrac{7a}{10} \Big \rgroup$

  3. $\Big \lgroup \dfrac{a}{2}, \dfrac{3a}{10} \Big \rgroup$

  4. $\Big \lgroup \dfrac{7a}{10}, \dfrac{3a}{2} \Big \rgroup$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice physics turning effects of forces stability and centre of mass center of mass centre of mass

Two blocks of masses $8$kg are connected by a spring of negligible mass and placed on a frictions less horizontal surface. An impulse gives a velocity of $12$m/s to the heavier block in the direction of lighter block. The velocity of the center of mass is:-

  1. $12$m/s

  2. $10$m/s

  3. $8$m/s

  4. $6$m/s
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Velocity of center of mass is $=\dfrac{m _1v _1+m _2v _2}{m _1+m _2}$


                                                $=\dfrac{8\times 12+8\times 0}{8+8}$


                                                $=\dfrac{96+0}{16}$

                                                $=6m/s$
Hence, the answer is $6m/s.$

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

A solid cylinder at rest at the top of an inclined plane of height 2.7 m rolls down without slipping. If the same cylinder has to slide down a frictionless inclined plane and acquire the same velocity as that acquired by the centre of mass of the rolling cylinder at the bottom of the inclined plane, the height of the inclined plane in meters should be 

  1. 2.2

  2. 1.2

  3. 1.6

  4. 1.8
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice physics turning effects of forces stability and centre of mass center of mass centre of mass

Find the coordination of center of mass of a uniform semicircle closed wire frame with respect to the origin which is at its center.The radius of the circular portion is R.                

  1. $\left( {\dfrac{{4R}}{{3\pi }},0} \right)$

  2. $\left( {\dfrac{{2R}}{{\pi }},0} \right)$

  3. $\left( {\dfrac{R}{{\pi + 2}},0} \right)$

  4. $\left( {\dfrac{2R}{{\pi + 2}},0} \right)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We know that, $x+cm=\cfrac{4}{\pi R^2}\int^0 _R{-t^2 dt}$

$=\cfrac{4}{\pi R^2}|-\cfrac{t^3}{R}|^0 _R=\cfrac{4}{\pi R^2}(\cfrac{R^3}{3})=\cfrac{4R}{3\pi}$
Thus, co-ordinates should be $=[\cfrac{4}{3\pi},0]$

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

Two particles having mass ratio n : 1 are interconnected by a light in extensible string that passes over a smooth pulley. If the system is released, then the acceleration of the centre of mass of the system is

  1. $( n - 1 ) ^ { 2 } g$

  2. $\left( \frac { n + 1 } { n - 1 } \right) ^ { 2 } g$

  3. $\left( \frac { n - 1 } { n + 1 } \right) ^ { 2 } g$

  4. $\left( \frac { n + 1 } { n - 1 } \right) 9$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given$,$

$\frac{{{m _1}}}{{{m _2}}} = \frac{n}{1} = n$
Each mass have the acceleration $a = \frac{{\left( {{m _1} - {m _2}} \right)}}{{{m _1} + {m _2}}}$
however ${{m _1}}$ which is heavier will have the will have acceleration ${{a _1}}$ vertically down while the lighter mass ${{m _2}}$ will have acceleration ${{a _2}}$ vertically up $ \to {a _2} =  - {a _1}$
The acceleration or the centre of mass of the system$,$ ${a _{cm}} = \frac{{{m _1}{a _1} + {m _2}{a _2}}}{{{m _1} + {m _2}}}$
given that ${a _2} =  - {a _1} \to {a _{cm}} = \frac{{\left( {{m _1} - {m _2}} \right){a _1}}}{{{m _1} + {m _2}}} = \frac{{{m _1} - {m _2}}}{{{m _1} + {m _2}}} \times \frac{{\left( {{m _1} - {m _2}} \right)g}}{{{m _1} + {m _2}}} = \frac{{{{\left( {{m _1} - {m _2}} \right)}^2}g}}{{{m _1} + {m _2}}}$
Since $\frac{{{m _1}}}{{{m _2}}} = n$ diving by ${{m _2}}$ and simplifying 
$ \Rightarrow {a _{cm}} = {\left( {\frac{{n - 1}}{{n + 1}}} \right)^2}g$
Hence,
option $(C)$ is correct answer.

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

A thin uniform rod of length l and m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of:

  1. $\dfrac{1}{6} \dfrac{l\omega}{g}$

  2. $\dfrac{1}{2} \dfrac{l^2\omega^2}{g}$

  3. $\dfrac{1}{6} \dfrac{l^2\omega^2}{g}$

  4. $\dfrac{1}{3} \dfrac{l^2\omega^2}{g}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

At lowest height

$E=\cfrac{1}{2}I \omega^2$
At maximum weight $\omega=0$
$E=mgh+0$ (his height from lower point)
By conservation of energy
$\cfrac{1}{2}I\omega^2=mgh\h=\cfrac{I\omega^2}{2mg}\h=\cfrac{ml^2\omega^2}{6mg}=\cfrac{l^2\omega^2}{6g}$

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

Six identical particles each of mass $m$ are arranged at the corners of a regular hexagon of side length $a$. If the mass of one of the particle is doubled, the shift in the centre of mass is

  1. $a$

  2. $\dfrac {6a}{7}$

  3. $\dfrac {a}{7}$

  4. $\dfrac {a}{\sqrt {3}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The center of mass of a regular hexagon with identical masses is at the center. If one mass m is doubled to 2m, the system is equivalent to the original system plus an additional mass m at that corner. The shift is (m * r) / (total mass), where r is the distance from the center. Total mass = 7m. Shift = (m * a) / 7m = a/7.

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

Centre of mass is a point 

  1. Which is geometric centre of a body

  2. From which distance of particles are same

  3. Where the whole mass of the body is supposed the

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The center of mass is the unique point where the weighted relative position of the distributed mass sums to zero. It is the point at which the entire mass of the body can be considered to be concentrated for the purpose of translational motion analysis.

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

The centre of mass of a rigid body always lies inside the body. Is this statement true or false?

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
No it's not necessary that the centre of mass of a body should lie inside the body. Consider a circular ring, its centre of mass lies at the center of the ring where there is no content of the body. So it can also lie outside the body .