Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

NTA Abhyas 2020 · Physics · Center of Mass, Momentum and Collision

An undeformed spring of spring constant k is connected to a bead of...

An undeformed spring of spring constant kk is connected to a bead of mass mm which can move along a frictionless rod as shown in the figure. If the particle strikes the& bead at an angle of 45°45 ° with the horizontal and sticks to it, then the maximum elongation of the spring after the collision is

An undeformed spring of spring constant k is connected to a bead of mass m which can move along a frictionless rod as

Options

  1. Av4m2k\dfrac{v}{4}\sqrt{\dfrac{m}{2k}}
  2. Bv2mk\dfrac{v}{2}\sqrt{\dfrac{m}{k}}
  3. Cv2m2k\dfrac{v}{2}\sqrt{\dfrac{m}{2k}}
  4. Dv4mk\dfrac{v}{4}\sqrt{\dfrac{m}{k}}

Correct answer

B. v2mk\dfrac{v}{2}\sqrt{\dfrac{m}{k}}

Step-by-step solution

Conserving the linear momentum of the system along the rod

mvcos⁡45∘=2mv1{mv \cos 45}^{∘} = 2{mv}_{1}

v1=v22{v}_{1} = \dfrac{\text{v}}{2 \sqrt{2}}

Applying work-energy theorem

−12kx2=−12(2m)(v22)2- \dfrac{1}{2} {kx}^{2} = - \dfrac{1}{2} \left(2 \text{m}\right) {\left(\dfrac{\text{v}}{2 \sqrt{2}}\right)}^{2}

⇒x=v2mk⇒ \text{x} = \dfrac{v}{2}\sqrt{\dfrac{m}{k}}

Practice Center of Mass, Momentum and Collision on Quantrex Academy →

More from Center of Mass, Momentum and Collision

Two identical bodies A and B of equal masses have initial velocities v_1 = 4 i m/s and… JEE Main 2026The position of center of mass of three masses 2 kg, 3 kg and 15 kg placed with respect… JEE Main 2026Two blocks of masses 2 kg and 1 kg respectively, are tied to the ends of a string which… JEE Main 2026The position of an object having mass 0.1 kg as a function of time t is given as r =… JEE Main 2026A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses… JEE Main 2026In a perfectly inelastic collision, two spheres made of the same material with masses 15… JEE Main 2026Given below are two statements : Statement I : For a mechanical system of many particles… JEE Main 2026In a scattering experiment, a particle of mass 2 m collides with another particle of mass… JEE Advanced 2025 Full Center of Mass, Momentum and Collision list All NTA Abhyas JEE Main PYQs