MCQ
A simple pendulum with length  $L$ and mass $m$ of the bob is vibrating with an amplitude $A$. The maximum tension in the string is
  • A
    $mg$
  • $mg\left[ {1 + {{\left( {\frac{A}{L}} \right)}^2}} \right]$
  • C
    $mg\left[ {1 + {{\left( {\frac{A}{2L}} \right)}^2}} \right]$
  • D
    $mg\left[ {1 - {{\left( {\frac{3A}{L}} \right)}^2}} \right]$

Answer

Correct option: B.
$mg\left[ {1 + {{\left( {\frac{A}{L}} \right)}^2}} \right]$
b
$\mathrm{T}_{\max }-\mathrm{mg}=\frac{\mathrm{mv}^{2}}{\mathrm{L}}$

$\mathrm{T}_{\max }=\mathrm{mg}+\frac{\mathrm{m}(\mathrm{A} \omega)^{2}}{\mathrm{L}^{2}}$

$=m g+\frac{m}{L} A^{2} \frac{g}{L}=m g\left[1+\frac{A^{2}}{L^{2}}\right]$

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

Similar questions

The amplitude of a particle executing $SHM$ is $4 \,cm$. At the mean position the speed of the particle is $16\, cm/sec$. The distance of the particle from the mean position at which the speed of the particle becomes $8\sqrt 3 \,cm/s,$ will be .... $cm$
One atomic mass units is equivalent to .............. $MeV$ energy.
A solid cube and a solid sphere both made of same material are completely submerged in water but to different depths. The sphere and the cube have same surface area. The buoyant force is
A sphere collides with another sphere of identical mass. After collision, the two spheres move. The collision is inelastic. Then the angle between the directions of the two spheres is
A slider block $A$ moves downward at a speed of $v_A = 2\ m/s$ , at an angle of $75^o$ with horizontal as shown in the figure. The velocity with respect to $A$ of the portion of belt $B$ between ideal pulleys $C$ and $D$ is $v_{CD/A} = 2\ m/s$ at an angle $\theta $ with the horizontal. The magnitude of velocity of portion $CD$ of the belt when $\theta  = 15^o$ is   .......... $m/s$
$A$ box of mass $m$ is released from rest at position $1$ on the frictionless curved track shown. It slides a distance $d$ along the track in time $t$ to reach position $2$, dropping a vertical distance $h$. Let $v$ and $a$ be the instantaneous speed and instantaneous acceleration, respectively, of the box at position $2$. Which of the following equations is valid for this situation?
At a place where the acceleration due to gravity is $10\,m\,{\sec ^{ - 2}}$ a force of $5\, kg-wt$ acts on a body of mass $10\, kg$ initially at rest. The velocity of the body after $4$ second is .......... $m/\sec^{-1}$
A transverse harmonic wave on a string is given by $y(x, t)=5 \sin (6 t+0.003 x)$ where $x$ and $y$ are in $cm$ and $t$ in $sec$. The wave velocity is $...........\,ms ^{-1}$.
Two particles $P_1$ and $P_2$ are moving with velocities $v_1$ and $v_2$ respectively. Which of the statement about their relative velocity $v_{12}$ is true?
A river is flowing with velocity $5\ km/hr$ as shown in the figure. A boat starts from $A$ and reaches the other bank by covering shortest possible distance . Velocity of boat in still water is $3\ km/ hr$. The distance boat covers is    ......... $m$