A particle of mass \(100\,g\) is projected at time \(t =0\) with a speed \(20\,ms ^{-1}\) at an angle \(45^{\circ}\) to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time \(t=2\,s\) is found to be \(\sqrt{ K }\,kg\,m ^2 / s\). The value of \(K\) is \(............\) \(\left(\right.\) Take \(\left.g =10\,ms ^{-2}\right)\)

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(B) \(800\)

Step-by-step Solution

Detailed explanation

\(\text { Use } \Delta L =\int \limits_0^{ t } \tau dt\)

\(L _0=\int \limits_0^2 mg \left( v _{ x } t \right) dt\)

\(= mg _{ x } \frac{ t ^2}{2}=(0.1)(10)(10 \sqrt{2}) \frac{2^2}{2}\)

\(=20 \sqrt{2}\)

\(=\sqrt{800}\,kgm ^2 / s\)

Same subject

Rods x and y of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points A and F are maintained at \( 100^{\circ}C \) and \( 40^{\circ}C \) respectively. Given the thermal conductivity of rod x is three times of that of rod y, the temperature at junction points B and E are (close to):

JEE Mains 2026 Easy
Electric field in a plane electromagnetic wave is given by \({E}=50 \sin \left(500 {x}-10 \times 10^{10} {t}\right) \,{V} / {m}\) The velocity of electromagnetic wave in this medium is : (Given \({C}=\) speed of light in vacuum)

JEE Mains 2021 Medium
A rod \(C D\) of thermal resistance \(10.0\; {KW}^{-1}\) is joined at the middle of an identical rod \({AB}\) as shown in figure, The end \(A, B\) and \(D\) are maintained at \(200^{\circ} {C}, 100^{\circ} {C}\) and \(125^{\circ} {C}\) respectively. The heat current in \({CD}\) is \({P}\) watt. The value of \({P}\) is ... .

JEE Mains 2021 Hard
A long, straight wire of radius \(a\) carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance \(\frac{a}{3}\) and \(2 a,\) respectively from the axis of the wire is

JEE Mains 2020 Hard
An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to \(.......\%\)

JEE Mains 2020 Hard
A body of mass \(0.5\, kg\) travels on straight line path with velocity \(v =\left(3 x ^{2}+4\right) m / s\). The net workdone by the force during its displacement from \(x =0\) to \(x =2\, m\) is\(.......J\)

JEE Mains 2022 Medium

Explore more questions on app

From JEE Mains

If the magnetic field in a plane electromagnetic wave is given by \(\overrightarrow{\mathrm{B}}=3 \times 10^{-8} \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} \mathrm{t}\right) \hat{\mathrm{j}}\; \mathrm{T}\) then what will be expression for electric field?

JEE Mains 2020 Easy
When a long glass capillary tube of radius \(0.015\;cm\) is dipped in a liquid, the liquid rises to a height of \(15\, cm\) within it. If the contact angle between the liquid and glass to clase to \(0^{\circ},\) the surface tension of the liquid, in \(milli\,Newton \;m ^{-1}\) is \(.....\) \(\left[\rho_{\text {(liquid) }}=900\; kg\,m ^{-3}, g =10\, ms ^{-2}\right]\) (Give answer in closest integer)

JEE Mains 2020 Medium
Consider the following statements:
A. The junction area of solar cell is made very narrow compared to a photo diode.
B. Solar cells are not connected with any external bias.
C. LED is made of lightly doped p-n junction.
D. Increase of forward current results in continuous increase of LED light intensity.
E. LEDs have to be connected in forward bias for emission of light.
Choose the correct answer from the options given below:

JEE Mains 2025 Easy

Explore more questions on app