Consider the following statements
Assertion $(A)$ : $A$ cyclist always bends inwards while negotiating a curve
Reason $(R)$ : By bending he lowers his centre of gravity Of these statements,
both $A$ and $R$ are true and $R$ is the correct explanation of $A$
both $A$ and $R$ are true but $R$ is not the correct explanation of $A$
$A$ is true but $R$ is false
$A$ is false but $R$ is true
$A$ particle of mass $3m$ is projected from the ground at some angle with horizontal. The horizontal range is $R$. At the highest point of its path it breaks into two pieces $m$ and $2m$. The smaller mass comes to rest and larger mass finally falls at a distance $x$ from the point of projection where $x$ is equal to
Two uniform plates of the same thickness and area but of different materials, one shaped like an isosceles triangle and the other shaped like a rectangle are joined together to form a composite body as shown in the figure alongside.If the centre of mass of the composite body is located at the mid-point of their common side, then the ratio between masses of the triangle to that of the rectangle is
As shown in figure, when a spherical cavity (centred at $\mathrm{O})$ of radius $1$ is cut out of a uniform sphere of radius $\mathrm{R} \text { (centred at } \mathrm{C}),$ the centre of mass of remaining (shaded) part of sphere is at $G$, i.e, on the surface of the cavity. $\mathrm{R}$ can be detemined by the equation
Two point masses of $0.3\, kg$ and $0.7\, kg$ are fixed at the ends of a rod of length $1.4\, m$ and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of
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