Mathematics in Physics

Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is

Three forces acting on a body are shown in the figure. To have the resultant force only along the $y$-direction, the magnitude of the minimum additional force needed is

$\mathrm{Assertion}A:$ If $A,B,C,D$ are four points on a semi-circular arc with a centre at $O$ such that $|\vec{AB}|=|\vec{BC}|=|\vec{CD}|.$Then,$\vec{AB}+\vec{AC}+\vec{AD}=4\vec{AO}+\vec{OB}+\vec{OC}$…

The length of a metallic wire is increased by $20%$ and its area of cross-section is reduced by $4%.$ The percentage change in resistance of the metallic wire is$________.$

Vectors $a\hat{i}+b\hat{j}+\hat{k}$and $2\hat{i}-3\hat{j}+4\hat{k}$are perpendicular to each other when $3a+2b=7$, the ratio of $a$ to $b$ is $\frac{x}{2}$. The value of $x$ is _____.

The radius of a sphere is measured to be $(7.50\pm\,0.85)\mathrm{cm}$. Suppose the percentage error in its volume is $x$. The value of $x$, to the nearest$x$,is ___ ?

A student determined Young's Modulus of elasticity using the formula $Y=\frac{MgL^{3}}{4\mathrm{bd}^{3}\delta\,}.$Thevalue of $g$ is taken to be $9.8ms^{-2}$without any significant error, his observations areas…

A vector has magnitude same as that of $\vec{A}=3\hat{j}+4\hat{j}$ and is parallel to $\vec{B}=4\hat{i}+3\hat{j}$. The $x$ and $y$components of this vector in first quadrant are $x$and $3$ respectively where $x=$____?

If the projection of $2\hat{i}+4\hat{j}-2\hat{k}$ on $\hat{i}+2\hat{j}+\alpha\,\hat{k}$ is zero. Then, the value of $\alpha\,$ will be

For three vectors $\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k}), \vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k})$ and $\vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k})$, if $\vec{A} \cdot(\vec{B} \times \vec{C})=0$, then value of $x$ is…

For $z=a^{2}x^{3}y^{\frac{1}{2}}$, where '$a$' is a constant. If percentage error in measurement of '$x$' and '$y$' are $4%$and $12%$, respectively, then the percentage error for '$z$' will be _____$%$.

Two particles are located at equal distance from origin. The position vectors of those are represented by $\bar{A}=2 \hat{i}+3 n \hat{j}+2 \hat{k}$ and $\bar{B}=2 \hat{i}-2 \hat{j}+4 p \hat{k}$, respectively. If both…