A rectangular frame is to be suspended symmetrically by two strin… - Vidyadip

MCQ

A rectangular frame is to be suspended symmetrically by two strings of equal length on two supports. It can be done in one of the following three ways;

The tension in the strings will be

A
The same in all cases.
B
Least in $(a).$
✓
Least in $(b)$.
D
Least in $(c).$

✓

Answer

Correct option: C.

Least in $(b)$.

According to the $\text{FBD}$ diagram of the rectangular frame.
Let $M$ be the mass of rectangular frame and $0$ be the angle which the tension $T$ in the string makes with the horizontal

Balancing vertical forces,
$2\text{T}\sin\theta-\text{mg}=0 [T$ is tension in the string$]$
$\Rightarrow2\text{T}\sin\theta=\text{mg}$
Total horizontal force will be zero because of equal and opposite forces balance each other $(\text{T}\cos\theta).$
Now from Eq. $(i), \text{T}=\frac{\text{mg}}{2\sin\theta}$
Here, we know $mg$ is constant.
$\Rightarrow\text{T}\propto\frac{1}{\sin\theta}$
$T$ is least if $\sin\theta$ has maximum value.
$\text{T}_\text{min}=\frac{\text{mg}}{2\sin\theta_\text{max}}\text{ (since,}\sin\theta_{\text{max}}=1)$
$\sin\theta_\text{max}=1\Rightarrow\theta=90^\circ$
So the correct option is option $(c).$
Hence, tension is least for the case $(b).$

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 Mechanical Properties of Solids→Mechanical Properties of Solids — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If the excess pressure inside a soap bubble is balanced by oil column of height $2\; mm$, then the surface tension of soap solution will be ($r = 1 \,cm$ and density $d = 0.8\, gm/cc$)

The wavelength of ultrasonic waves in air is of the order of:

A car travelling at a speed of $30\, km/hour$ is brought to a halt in $8\, m$ by applying brakes. If the same car is travelling at $60 \,km/hour$, it can be brought to a halt with the same braking force in ............... $\mathrm{m}$

A solid sphere spinning about a horizontal axis with an angular velocity $\omega$ is placed on a horizontal surface. Subsequently it rolls without slipping with an angular velocity of

If T is the total time of flight, $h$ is the maximum height $ \& R$ is the range for horizontal motion, the $x$ and $y$ co-ordinates of projectile motion and time $t$ are related as

A diwali rocket is ejecting $0.05\, kg$ of gases per second at a velocity of $400\, m/sec$ . The accelerating force on the rocket is

Which of the following statements is correct

For a ball falling in a liquid with constant velocity, ratio of resistance force due to the liquid to that due to gravity is:

Two parallel wires carry currents of 20A and 40A in opposite directions. Another wire carying a current anti parallel to 20A is placed midway between the two wires. T he magnetic force on it will be:

Two pulley arrangements of figure given are identical. The mass of the rope is negligible. In fig $(a)$, the mass $m$ is lifted by attaching a mass $2\,m$ to the other end of the rope. In fig $(b)$, $m$ is lifted up by pulling the other end of the rope with a constant downward force $F = 2mg$. The acceleration of $m$ in the two cases are respectively