A frictionless pulley is attached to one arm of a balance and a s… - Vidyadip

MCQ

A frictionless pulley is attached to one arm of a balance and a string passed around it carries two masses $m_1$ and $m_2$. The pulley is provided with $a$ clamp due to which $m_1$ and $m_2$ do not move $w.r.t.$ each other. On removing the clamp, $m_1$ and $m_2$ start moving. How much change in counter mass has to be made to restore balance?

A
$\frac{{{{({m_1} + {m_2})}^2}}}{{{m_1} - {m_2}}}$
✓
$\frac{{{{({m_1} - {m_2})}^2}}}{{{m_1} + {m_2}}}$
C
$2m_1 -m_2$
D
$m_1 -m_2$

✓

Answer

Correct option: B.

$\frac{{{{({m_1} - {m_2})}^2}}}{{{m_1} + {m_2}}}$

b
When the clamp is removed, the pull on the left arm (i.e., tension) $=$ $\frac {4 \mathrm{m}_{1} \mathrm{m}_{2} \mathrm{g}} {\left(\mathrm{m}_{1}+\mathrm{m}_{2}\right)}$

When the clamp is not removed, the tension

$=\left(m_{1}+m_{2}\right) g$

$\mathrm{W}=$ Increase in counter weight

$=\frac{4 m_{1} m_{2} g}{\left(m_{1}+m_{2}\right)}-\left(m_{1}+m_{2}\right) g=-\frac{\left(m_{1}-m_{2}\right)^{2}}{\left(m_{1}+m_{2}\right)} g$

Decrease in counter weight $=\frac{\left(m_{1}-m_{2}\right)^{2} g}{\left(m_{1}+m_{2}\right)}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 4.1 , newtons laws of motion→4.1 , newtons laws of motion — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A particle executes simple hormonic motion between $x =\, -A$ and $x = +A$ . It starts from $x = 0$ moves in $+x-$ direction. The time taken for it to move from $x = 0$ to $x = \frac {A}{2}$ is $T_1$ and to move from $\frac {A}{2}$ to $\frac {A}{\sqrt 2}$ is $T_2$ , then

According to the law of energy equalization the value of average energy of a molecule of diatomic gas will be:

If $250 \,J$ of work is done in sliding a $5 \,kg$ block up an inclined plane of height $4 \,m$. value of Work done against friction is ............. $J$ $\left(g=10 \,ms ^{-2}\right)$

Which is the quantity which remains conserved in both elastic and inelastic collisions?

The angle between vector $(\overrightarrow{{A}})$ and $(\overrightarrow{{A}}-\overrightarrow{{B}})$ is :

A cylindrical tube of uniform cross-sectional area $A$ is fitted with two air tight frictionless pistons. The pistons are connected to each other by a metallic wire. Initially the pressure of the gas is $P_0$ and temperature is $T_0$, atmospheric pressure is also $P_0$. Now the temperature of the gas is increased to $2T_0$, the tension in the wire will be

A car is moving on a circular path of radius $500\ m$ with speed $30\ m/s$ and speed is increasing at rate $2\ m/s^2$ net acceleration will be ......... $m/s^2$

Let E, G and N represent the magnitudes of electromagnetic gravitational and nuclear forces between two electrons at a given separation. Then:

Two cubical blocks identical in dimensions float in water in such a way that $1$ st block floats with half part immersed in water and second block floats with $3 / 4$ of its volume inside the water. The ratio of densities of blocks is ..........

A $140\, g$ ball, in horizontal flight with a speed $v_1$ of $39.0\, m/s$, is struck by a bat. After leaving the bat, the ball travel in the opposite direction with speed $v_2 = 39.0\, m/s$. If the impact time $\Delta t$ for the ball-bat collision is $1.20\, ms$, what average net force acts on the ball ......... $N$