Two blocks of masses m1 and m2 being connected with a light spring of stiffness k are driven with forces F1 and F2 on a smooth horizontal plane. If the blocks move with same acceleration a0, the value of a0 is:-

Question

Two blocks of masses m1 and m2 being connected with a light spring of stiffness k are driven with forces F1 and F2 on a smooth horizontal plane. If the blocks move with same acceleration a0, the value of a0 is:- <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-5ap8vnedmhjwlge9.jpg" /> (A) (F1 - F2/ m1 + m2) (B) (F1 m2 - m1 F2/( m1 + m2)2) (C) (1/2)((F1/ m1) + (F2/ m2)) (D) decided by the stiffness of the spring

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-5ap8vnedmhjw9ys2.jpg" /> In the given system, the spring force due to spring on the masses is internal force. The acceleration of system is due to external forces only. Here we can assume the two blocks as one system and their acceleration is given as a0=( textNet force towards motion of masses/ textTotal mass) a0=(F1 - F2/m1 + m2) .

Q. Two blocks of masses $m_{1}$ and $m_{2}$ being connected with a light spring of stiffness $k$ are driven with forces $F_{1}$ and $F_{2}$ on a smooth horizontal plane. If the blocks move with same acceleration $a_{0},$ the value of $a_{0}$ is:-

$\frac{F _{1} - F _{2}}{m _{1} + m _{2}}$

$\frac{F _{1} m _{2} - m _{1} F _{2}}{( m _{1} + m _{2} ) ^{2}}$

$\frac{1}{2} (\frac{F _{1}}{m _{1}} + \frac{F _{2}}{m _{2}})$

decided by the stiffness of the spring

Q. Two blocks of masses m1​ and m2​ being connected with a light spring of stiffness k are driven with forces F1​ and F2​ on a smooth horizontal plane. If the blocks move with same acceleration a0​, the value of a0​ is:-

m1​+m2​F1​−F2​​

(m1​+m2​)2F1​m2​−m1​F2​​

21​(m1​F1​​+m2​F2​​)

decided by the stiffness of the spring

Q. Two blocks of masses $m_{1}$ and $m_{2}$ being connected with a light spring of stiffness $k$ are driven with forces $F_{1}$ and $F_{2}$ on a smooth horizontal plane. If the blocks move with same acceleration $a_{0},$ the value of $a_{0}$ is:-

$\frac{F _{1} - F _{2}}{m _{1} + m _{2}}$

$\frac{F _{1} m _{2} - m _{1} F _{2}}{( m _{1} + m _{2} ) ^{2}}$

$\frac{1}{2} (\frac{F _{1}}{m _{1}} + \frac{F _{2}}{m _{2}})$