Download App

Linear Equations in Two Variables — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsLinear Equations in Two Variables4 Marks
Question
The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of two variables and draw the graph of the same by taking the constant mass equal to $6 \ kg$. Read from the graph, the force required when the acceleration produced is:
$i. 5\ ms^{-2}$
$ii.\ ms^{-2}$
✓

Answer

Given that, the force $(F)$ is directly proportional to the the acceleration $(a)$
i.e. $\text{F}\propto\text{a}$
$\Rightarrow\text{F}=\text{ma} [$where $m =$ arbitary constant and take value $6\ kg$ of mass$]$ $\therefore\text{F}=6\text{a}$
$i.$ If $\text{a}=5\frac{\text{m}}{\text{s}}^2$ then from $Eq (i),$ we get
$F = 6 \times 5 = 30N$
$ii.$ If $\text{a}=6\frac{\text{m}}{\text{s}}^2$ then from $Eq (i),$ we get
$F = 6 \times 6 = 36N$
Here, we find two points $A(5, 30)$ and $B(6, 36).$
So draw the graph by plotting the point and joining the line $AB.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks Questions" from Linear Equations in Two Variables→Linear Equations in Two Variables — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

Using factor theorem, factorize the following polynomials: $x^4 - 7x^3_+ 9x^2 + 7x - 10$
→
Two cones have their heights in the ratio $1 : 3$ and the radii of their bases in the ratio $3 : 1$. Find the ratio of their volumes.
→
In a parallelogram $ABCD$, the bisector of $\angle\text{A}$ also bisects $BC$ at $X$. Find $AB : AD$.
→
In a $\triangle\text{ABC, D}$ is the midpoint of side $AC$ such that $\text{BD}=\frac{1}{2}\text{AC}.$ Show that $\angle\text{ABC}$ is a right angle.
→
In the adjoining figure, ABCD is a square and $\triangle\text{EDC}$ is an equilateral triangle. Prove that:
  1. AE = BE,
  2. $\angle\text{DAE}=15^{\circ}.$
→
In the given figure, BD = DC and $\angle\text{CBD}=30^\circ,$ find $\angle\text{BAC}.$
→
A cylinder and a cone have equal radii of their base and equal heights. If their curved surface area are in the ratio $8 : 5$, show that the radius of each is to the height of each as $3 : 4$
→
The curved surface area of a cylinder is $4400\ cm^2$ and the circumference of its base is $110\ cm$ . Find the height and the volume of the cylinder.
→
The ratio between the curved surface area and the total surface area of a right circular cylinder is $1: 2$. Find the volume of the cylinder, if its total surface area is $616cm^2.$
→
Simplify: $\frac{4+\sqrt{5}}{4-\sqrt{5}}+\frac{4-\sqrt{5}}{4+\sqrt{5}}$
→