enEnglishguગુજરાતી
JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
A bullet of mass \(10\, g\) and speed \(500\, m/s\) is fired into a door and gets embedded exactly at the centre of the door. The door is \(1.0\, m\) wide and weighs \(12\, kg\). It is hinged at one end and rotates about a vertical axis practically without friction . The angular speed of the door just after the bullet embeds into it will be
- A \(6.25\, rad/sec\)
- B \(0.625\, rad/sec\)
- C \(3.35\, rad/sec\)
- D \(0.335\, rad/sec\)
Answer & Solution
Correct Answer
(B) \(0.625\, rad/sec\)
Step-by-step Solution
Detailed explanation
Angular momentum imparted by the bullet \(L = mv \times r \)\( = \left( {10 \times {{10}^{ - 3}}} \right) \times 500 \times \frac{1}{2} = 2.5\) \(I = \frac{{M{L^2}}}{3} = \frac{{12 \times {{1.0}^2}}}{3} = 4kg{m^2}\) \(L = I\omega \)…
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
- The series combination of two batteries, both of the same emf \(10 \mathrm{\;V},\) but different internal resistance of \(20\; \Omega\) and \(5\; \Omega,\) is connected to the parallel combination of two resistors \(30\; \Omega\) and \(\mathrm{R}\; \Omega .\) The voltage difference across the battery of internal resistance \(20\; \Omega\) is zero, the value of \(\mathrm{R}(\text { in } \Omega)\) isJEE Mains 2020 Hard
- A piece of wood from a recently cut tree shows \(20\,decays\) per minute. A wooden piece of same size placed in a museum ( obtained from a tree cut many years back) shows \(2\,decays\) per minute. If half life of \(C^{14}\) is \(5730\, years\), then age of the wooden piece placed in the museum is approximately ........... \(years\)JEE Mains 2014 Hard
- The electric field between the two parallel plates of a capacitor of \(1.5 \mu \mathrm{F}\) capacitance drops to one third of its initial value in \(6.6 \mu \mathrm{s}\) when the plates are connected by a thin wire. The resistance of this wire is _______ \(\Omega\). (Given, \(\log 3=1.1)\)JEE Mains 2024 Hard
- An inductor of \(0.5 \,mH\), a capacitor of \(200 \,\mu F\) and a resistor of \(2 \,\Omega\) are connected in series with a \(220 \,V\) ac source. If the current is in phase with the emf, the frequency of ac source will be ................ \(\times 10^{2} \,Hz\)JEE Mains 2022 Hard
- Consider a Young’s double slit experiment as shown in figure. What should be the slit separation \(d\) in terms of wavelength \(\lambda \) such that the first minima occurs directly in front of the slit \((S_1)\)?
JEE Mains 2019 Hard - In a radioactive material, fraction of active material remaining after time \(t\) is \(\frac{9}{16}\) The fraction that was remaining after \(\frac{t}{2}\) isJEE Mains 2020 Medium
More PYQs from JEE Mains
- The value of the integral \( I=\int_{\frac{\pi}{24}}^{\frac{5\pi}{24}}\frac{dx}{1+\sqrt[3]{\tan 2x}} \) is:JEE Mains 2026 Hard
- In the given circuit, value of \(Y\) is
JEE Mains 2020 Medium - Suppose \(\quad f : R \rightarrow(0, \infty)\) be a differentiable function such that \(5 f ( x + y )= f ( x ) \cdot f ( y ), \forall x , y \in R\). If \(f(3)=320\), then \(\sum \limits_{n=0}^5 f(n)\) is equal to :JEE Mains 2023 Hard
- Let \(\vec{a}=6 \hat{i}+9 \hat{j}+12 \hat{k}, \vec{b}=\alpha \hat{i}+11 \hat{j}-2 \hat{k}\) and \(\vec{c}\) be vectors such that \(\vec{a} \times \vec{c}=\vec{a} \times \vec{b}\). If \(\vec{a} \cdot \vec{c}=-12\), \(\vec{c} .(\hat{i}-2 \hat{j}+\hat{k})=5\), then \(\vec{c} \cdot(\hat{i}+\hat{j}+\hat{k})\) is equal to \(.............\).JEE Mains 2023 Hard
- Let \(A=\left[\begin{array}{ll}x & 1 \\ 1 & 0\end{array}\right], x \in R\) and \(A^{4}=\left[a_{i j}\right] .\) If \(a_{11}=109,\) then \(a_{22}\) is equal toJEE Mains 2020 Hard
- A charge \(q\) is spread uniformly over an insulated loop of radius \(r\) . If it is rotated with an angular velocity \(\omega \) with respect to normal axis then the magnetic moment of the loop isJEE Mains 2018 Medium