TS EAMCET · Physics · Mathematics in Physics
If \(\mathbf{r}_1=2 \hat{\mathbf{x}}, \mathbf{r}_2=2 \hat{\mathbf{y}}\), where \(\hat{\mathbf{x}}\) and \(\hat{\mathbf{y}}\) are unit vectors along the \(X\)-axis and \(Y\)-axis respectively, then the magnitude of \(\mathbf{r}_1+\mathbf{r}_2\) is
- A \(2 \sqrt{2}\)
- B \(2 \sqrt{3}\)
- C \(3 \sqrt{2}\)
- D \(\sqrt{3}\)
Answer & Solution
Correct Answer
(A) \(2 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
\begin{array}{ll}\text { Given, } \mathbf{r}_1=2 \hat{\mathbf{x}} \Rightarrow \mathbf{r}_2=2 \hat{\mathbf{y}} \\\therefore \mathbf{r}_1+\mathbf{r}_2=2 \hat{\mathbf{x}}+2 \hat{\mathbf{y}} \\ \therefore \left|\mathbf{r}_1+\mathbf{r}_2\right|=\sqrt{2^2+2^2}=\sqrt{8}=2…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- Two points \(A\) and \(B\) on the axis of a circular current loop are at distances of 4 cm and \(3 \sqrt{3} \mathrm{~cm}\) from the centre of the loop. If the ratio of the induced magnetic fields at points \(A\) and \(B\) is \(216: 125\), the radius of the loop isTS EAMCET 2024 Medium
- A ray of light incidents at an angle of \(9.3^{\circ}\) on one face of a small angle prism of refracting angle \(6^{\circ}\). If the ray of light emerges normally from the second face, the refractive index of the material of the prism isTS EAMCET 2025 Medium
-
An alphabet ' \(T\) ' made of two similar thin uniform metal plates of each length ' \(L\) ' and width ' \(a\) ' is placed on a horizontal surface as shown in the figure. If the alphabet is vertically inverted, the shift in the position of its centre of mass from the horizontal surface isTS EAMCET 2024 Hard - If \(V_0\) is the volume of a standard unit cell of germanium crystal containing \(N_0\) atoms, then the expression for the mass \(m\) of a volume \(V\) in terms of \(V_0, N_0, M_{\text {mol }}\) and \(N_A\) is [here, \(M\) is the molar mass of germanium and \(N_A\) is the Avogadro's constant]TS EAMCET 2018 Easy
- The following figure shows a Carnot engine that works between temperatures and and drives a Carnot refrigeration that works between temperatures and The quantity will be
TS EAMCET 2021 Hard - \(L C R\) circuit, the resonance frequency of circuit increases two times of the initial circuit by changing \(C\) and \(C^{\prime}\) and \(R\) from \(100 \Omega\) to \(400 \Omega\), while the inductance was kept the same. The ratio \(C / C^{\prime}\), isTS EAMCET 2019 Medium
More PYQs from TS EAMCET
- When a force \(F_1\) is applied on a metallic wire, the length of the wire is \(L_1\). If a force \(F_2\) is applied on the same wire, the length of the wire is \(L_2\). The original length of the wire \(L\) isTS EAMCET 2015 Easy
- The length of a pendulum is measured as \(1.01 \mathrm{~m}\) and time for 30 oscillations is measured as one minute \(3 \mathrm{~s}\). Error length is \(0.01 \mathrm{~m}\) and error in time is \(3 \mathrm{~s}\). The percentage error in the measurement of acceleration due to gravity isTS EAMCET 2012 Easy
- A circular coil carrying a current of 2.5 A is free to rotate about an axis in its plane perpendicular to an external magnetic field. When the coil is made to oscillate, the time period of oscillation is \(T\). If the current through the coil is 10 A , the time period of oscillation isTS EAMCET 2024 Easy
- The frequency of light emitted, when the electron makes transition from the level of principle quantum number \(n=2\) to the level with \(n=1\) is (Take, the ionization energy of hydrogen to be \(13.6 \mathrm{eV}\) and \(h \simeq 4 \times 10^{-15} \mathrm{eV}\)-s)TS EAMCET 2018 Easy
- In a travelling plane electromagnetic wave, the maximum magnetic field is \(1.26 \times 10^{-4} \mathrm{~T}\). The intensity of the wave is (Assume, \(\mu_0=1.26 \times 10^{-6} \mathrm{H} / \mathrm{m}\) )TS EAMCET 2019 Easy
- Three capacitors of capacitances \(10 \mu \mathrm{~F}, 5 \mu \mathrm{~F}\) and \(20 \mu \mathrm{~F}\) are connected in series with a 14 V dc supply. The charge on \(5 \mu \mathrm{~F}\) capacitor isTS EAMCET 2024 Easy