A square shaped hole of side $l=\frac{a}{2}$ is carved out at a distance $d =\frac{ a }{2}$ from the centre $'O'$ of a uniform circular disk of radius $a$. If the distance of the centre of mass of the remaining portion from $O$ is $-\frac{a}{X},$ value of $X$ (to the nearest integer) is.......
A square shaped hole of side $l=\frac{a}{2}$ is carved out at a distance $d =\frac{ a }{2}$ from the centre $'O'$ of a uniform circular disk of radius $a$. If the distance of the centre of mass of the remaining portion from $O$ is $-\frac{a}{X},$ value of $X$ (to the nearest integer) is.......
- [JEE MAIN 2020]
- A
$15$
- B
$45$
- C
$30$
- D
$23$
Similar Questions
A thin bar of length $L$ has a mass per unit length $\lambda $, that increases linearly with distance from one end. If its total mass is $M$ and its mass per unit length at the lighter end is $\lambda_0$, then the distance of the centre of mass from the lighter end is
A thin bar of length $L$ has a mass per unit length $\lambda $, that increases linearly with distance from one end. If its total mass is $M$ and its mass per unit length at the lighter end is $\lambda_0$, then the distance of the centre of mass from the lighter end is
- [JEE MAIN 2014]
Obtain the general expression of centre of mass for distributed $n$ particles of system in three dimension.
Obtain the general expression of centre of mass for distributed $n$ particles of system in three dimension.
$(a)$ Centre of gravity $(C.G.)$ of a body is the point at which the weight of the body acts.
$(b)$ Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius
$(c)$ To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its $C.G.$
$(d)$ The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the $C.G.$ of the body to the axis of rotation.
Which one of the following pairs of statements is correct ?
$(a)$ Centre of gravity $(C.G.)$ of a body is the point at which the weight of the body acts.
$(b)$ Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius
$(c)$ To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its $C.G.$
$(d)$ The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the $C.G.$ of the body to the axis of rotation.
Which one of the following pairs of statements is correct ?
- [AIPMT 2010]
A carpenter has constructed a toy as shown in the adjoining figure. If the density of the material of the sphere is $12$ times that of cone, the position of the centre of mass of the toy is given by
A carpenter has constructed a toy as shown in the adjoining figure. If the density of the material of the sphere is $12$ times that of cone, the position of the centre of mass of the toy is given by
In the $HCl$ molecule, the separation between the nuclet of the two atoms is about $1.27 \;\mathring A\left(1\; \mathring A=10^{-10} \;m \right) .$ Find the approximate location of the $CM$ of the molecule. given that a chlorine atom is about $35.5$ times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.
In the $HCl$ molecule, the separation between the nuclet of the two atoms is about $1.27 \;\mathring A\left(1\; \mathring A=10^{-10} \;m \right) .$ Find the approximate location of the $CM$ of the molecule. given that a chlorine atom is about $35.5$ times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.