Question

A block A of mass M = 2kg is connected to another block B of mass 1 kg with a string and a spring of force constant k = 600 N/m as shown in the figure. Initially spring is compressed to 10 cm and whole system is moving on a smooth surface with a velocity v = 1 m/s. At any time thread is burnt, the velocity of block A, when B is having maximum velocity w.r.t. ground, is –

• A. Zero
• B. 1 m/s
• C. 3 m/s
• D. None of these

Answer 1

Answer: (A)

Zero

Answer 2

In CM frame : -

mv_l = Mv₂ ; v_l = 2v₂

from COE,

$\frac { 1 } { 2 }$ $\operatorname { mv } _ { 1 } ^ { 2 }$ + $\frac { 1 } { 2 } \mathrm { Mv } _ { 2 } ^ { 2 } = \frac { 1 } { 2 } \mathrm { k } \ell _ { 0 } ^ { 2 }$ ̃ $2 \mathrm { v } _ { 2 } ^ { 2 } + \mathrm { v } _ { 2 } ^ { 2 } = \frac { 1 } { 2 } \mathrm { k } \ell _ { 0 } ^ { 2 }$

v₂ = 0.1 × 10 = 1 m/s in –x direction

In ground frame

VM = – v₂ + v = 0