JEE Mains · Physics · STD 11 - 4.1 newtons laws of motion
A simple pendulum of length \(1 \mathrm{~m}\) has a wooden bob of mass \(1 \mathrm{~kg}\). It is struck by a bullet of mass \(10^{-2} \mathrm{~kg}\) moving with a speed of \(2 \times 10^2 \mathrm{~ms}^{-1}\). The bullet gets embedded into the bob. The height to which the bob rises before swinging back is _______. (use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )
- A \(0.30 \mathrm{~m}\)
- B \(0.20 \mathrm{~m}\)
- C \(0.35 \mathrm{~m}\)
- D \(0.40 \mathrm{~m}\)
Answer & Solution
Correct Answer
(B) \(0.20 \mathrm{~m}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{mu}=(\mathrm{M}+\mathrm{m}) \mathrm{V}\) \(10^{-2} \times 2 \times 10^2 \cong 1 \times \mathrm{V}\) \(\mathrm{V} \cong 2 \mathrm{~m} / \mathrm{s}\) \(\mathrm{h}=\frac{\mathrm{V}^2}{2 \mathrm{~g}}=0.2 \mathrm{~m}\)
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
- A particle initially at rest starts moving from reference point. \(\mathrm{x}=0\) along \(\mathrm{x}\)-axis, with velocity \(v\) that varies as \(v=4 \sqrt{\mathrm{x} m} / \mathrm{s}\). The acceleration of the particle is _______ \( \mathrm{ms}^{-2}\).JEE Mains 2024 Hard
- In the potentiometer, when the cell in the secondary circuit is shunted with 4 \(\Omega\) resistance, the balance is obtained at the length 120 cm of wire. Now when the same cell is shunted with 12 \(\Omega\) resistance, the balance is shifted to a length of 180 cm. The internal resistance of cell is ___________ \(\Omega\).JEE Mains 2026 Medium
- A particle starts from the origin at \(\mathrm{t}=0\) with an initial velocity of \(3.0 \hat{\mathrm{i}} \;\mathrm{m} / \mathrm{s}\) and moves in the \(x-y\) plane with a constant acceleration \((6.0 \hat{\mathrm{i}}+4.0 \hat{\mathrm{j}}) \;\mathrm{m} / \mathrm{s}^{2} .\) The \(\mathrm{x}\) -coordinate of the particle at the instant when its \(y-\)coordinate is \(32\;\mathrm{m}\) is \(D\) meters. The value of \(D\) isJEE Mains 2020 Medium
- A particle starts from origin at \(t=0\) with a velocity \(5 \hat{i} \mathrm{~m} / \mathrm{s}\) and moves in \(x-y\) plane under action of a force which produces a constant acceleration of \((3 \hat{i}+2 \hat{j}) \mathrm{m} / \mathrm{s}^2\). If the \(x\)-coordinate of the particle at that instant is \(84 \mathrm{~m}\), then the speed of the particle at this time is \(\sqrt{\alpha} \mathrm{m} / \mathrm{s}\). The value of \(\alpha\) is___________.JEE Mains 2024 Hard
- One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, \(27\,^oC\).The work done on the gas will beJEE Mains 2018 Medium
- The equation of a particle executing simple harmonic motion is given by \(x =\sin \pi\left( t +\frac{1}{3}\right) m\). At \(t =1 \,s\), the speed of particle will be .......... \(cm s ^{-1}\) (Given : \(\pi=3.14\) )JEE Mains 2022 Medium
More PYQs from JEE Mains
- The number of real solutions of the equation \(e ^{4 x }+4 e ^{3 x }-58 e ^{2 x }+4 e ^{ x }+1=0\) is..........JEE Mains 2022 Hard
- A triangular plate is shown. A force \(\overrightarrow{ F }=4 \hat{ i }-3 \hat{ j }\) is applied at point \(P\). The torque at point \(P\) with respect to point \('O'\) and \('Q'\) are
JEE Mains 2021 Hard - \(\text { If } \int \frac{1}{\sqrt[5]{(x-1)^4(x+3)^6}} d x=A\left(\frac{\alpha x-1}{\beta x+3}\right)^B+C,\) where \(\mathrm{C}\) is the constant of integration, then the value of \(\alpha+\beta+20 \mathrm{AB}\) is ...........JEE Mains 2024 Hard
- If \(\mathrm{n}\) is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then \(\mathrm{n}\) is equal to :JEE Mains 2024 Medium
- Let a line \(\mathrm{y}=\mathrm{mx}(\mathrm{m}>0)\) intersect the parabola, \(\mathrm{y}^{2}=\mathrm{x}\) at a point \(\mathrm{P},\) other than the origin. Let the tangent to it at \(P\) meet the \(x\) -axis at the point \(Q\). If area \((\Delta \mathrm{OPQ})=4\) sq. units, then \(\mathrm{m}\) is equal toJEE Mains 2020 Hard
- Let \(f(x)=\int_0^x g(t) \log _e\left(\frac{1-t}{1+t}\right) d t\), where \(g\) is a continuous odd function. If \(\int_{-\pi / 2}^{\pi / 2}\left(f(x)+\frac{x^2 \cos x}{1+e^x}\right) d x=\left(\frac{\pi}{\alpha}\right)^2-\alpha\), then \(\alpha\) is equal to ..............JEE Mains 2024 Hard