A T shaped object with dimensions shown in th | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

For translatory motion the force should be applied

on the centre of mass of the body. So we have to

calculate the location of centre of mass of

Vedclass · Accepted Answer

$\frac {4}{3}\,l$

Vedclass · Answer

For translatory motion the force should be applied

on the centre of mass of the body. So we have to

calculate the location of centre of mass of $\mathrm{&lsquo;T&rsquo;}$

shaped object.

Let mass of rod $\mathrm{AB}$ in $\mathrm{m}$ so the mass of $\mathrm{rod} \mathrm{CD}$

will be $2 \mathrm{m}$

Let $y_{1}$ is the centre of mass of rod $A B$ and $y_{2}$ is

the centre of mass of rod $CD.$ We can consider

that whole mass of the rod is placed at their respect

at their respective centre of mass i.e.. mass $\mathrm{m}$ is

placed at $y_{1}$ and mass $2 m$ is placed at $y_{2}$

Taking point $C$ at the origin position vector

 of point $y_{1}$ and $y_{2}$ can be written as

$\overrightarrow {{f_1}}  = \ell \hat j,\overrightarrow {{f_2}}  = \ell \hat j.\,\,and\,\,{m_1} = m\,\,and\,\,{m_2} = 2m$

Position vector of centre of mass of the system

${\overrightarrow f _{cm}} = \frac{{{m_1}\overrightarrow {{r_1}}  + {m_2}\overrightarrow {{r_2}} }}{{{m_1} + {m_2}}} = \frac{{{m_2}\ell \hat j + 2m\ell \hat j}}{{m + 2m}} = \frac{{4m\ell \hat j}}{{3m}} = \frac{4}{3}\ell \hat j$

Hence the distance of centre of mass from

$C=\frac{4}{3} \ell$

A $T$ shaped object with dimensions shown in the figure, is lying a smooth floor. A force $'\vec F'$ is applied at the point $P$ parallel to $AB,$ such that the object has only the translational motion without rotation. Find the location of $P$ with respect to $C$

Similar Questions

A circular disc is rolling on a horizontal plane. Its total kinetic energy is $300\,J$ . ....... $J$ is its translational $K.E$

$A$ car travelling on a smooth road passes through $a$ curved portion of the road in form of an arc of circle of radius $10 m$. If the mass of car is $500\, kg$, the reaction on car at lowest point $P$ where its speed is $20 m/s$ is ......... $kN$.

Three bodies , a ring, a solid cylinder and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical. Which of the bodies reaches the ground with maximum velocity?

If the angular momentum of a body is increased by $200\,\%$ then increase in its rotational kinetic energy will be ....... $\%$.