Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Physics-

General

Easy

Question

A uniform rod of length $L$ and mass $M$ is pivoted at the centre. Its two ends are attached to two springs of equal spring constant $k.$ The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle $theta$ in one direction and released. The frequency of oscillation is

$\frac{1}{2 π} \sqrt{\frac{2 k}{M}}$
$\frac{1}{2 π} \sqrt{\frac{k}{M}}$
$\frac{1}{2 π} \sqrt{\frac{6 k}{M}}$
$\frac{1}{2 π} \sqrt{\frac{24 k}{M}}$

The correct answer is: $fraction numerator 1 over denominator 2 pi end fraction square root of fraction numerator 6 k over denominator M end fraction end root$

Torque about $blank P equals negative open parentheses k x close parentheses fraction numerator L over denominator 2 end fraction plus open parentheses negative k x fraction numerator L over denominator 2 end fraction close parentheses equals negative k x L equals negative k fraction numerator L to the power of 2 end exponent over denominator 2 end fraction theta$
For small angle $theta comma blank x equals fraction numerator L over denominator 2 end fraction theta semicolon blank tau equals negative I alpha$

$rightwards double arrow negative fraction numerator K L to the power of 2 end exponent over denominator 2 end fraction theta equals fraction numerator M L to the power of 2 end exponent over denominator 12 end fraction alpha$
$rightwards double arrow fraction numerator negative 6 K theta over denominator M end fraction equals alpha$
$rightwards double arrow omega equals square root of fraction numerator 6 K over denominator M end fraction end root$ and $f equals fraction numerator omega over denominator 2 pi end fraction equals fraction numerator 1 over denominator 2 pi end fraction square root of fraction numerator 6 K over denominator M end fraction end root$

Related Questions to study

The frequency of oscillation of the springs shown in the figure will be

The frequency of oscillation of the springs shown in the figure will be

physics-General

The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is

The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is

physics-General

A small block is connected to one end of a massless spring of un-stretched length $4.9 m$ . The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by $0.2 m$ and released from rest at $t equals 0.$ It then executes simple harmonic motion with angular frequency $omega equals fraction numerator pi over denominator 3 end fraction r a d divided by s.$ Simultaneously at $t equals 0 comma$ a small pebble is projected with speed $v$ frompoint $P$ is at angle of $45 degree$ as shown in the figure. Point $P$ is at a horizontal distance of $10 blank m$ from $O.$ If the pebble hits the block at $t equals 1 s comma$ the value of $v$ is (take $g equals 10 m divided by s to the power of 2 end exponent$ )

A small block is connected to one end of a massless spring of un-stretched length $4.9 m$ . The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by $0.2 m$ and released from rest at $t equals 0.$ It then executes simple harmonic motion with angular frequency $omega equals fraction numerator pi over denominator 3 end fraction r a d divided by s.$ Simultaneously at $t equals 0 comma$ a small pebble is projected with speed $v$ frompoint $P$ is at angle of $45 degree$ as shown in the figure. Point $P$ is at a horizontal distance of $10 blank m$ from $O.$ If the pebble hits the block at $t equals 1 s comma$ the value of $v$ is (take $g equals 10 m divided by s to the power of 2 end exponent$ )

physics-General

parallel

A small block is connected to one end of a massless spring of un-stretched length $4.9 m$ . The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by $0.2 m$ and released from rest at $t equals 0.$ It then executes simple harmonic motion with angular frequency $omega equals fraction numerator pi over denominator 3 end fraction r a d divided by s.$ Simultaneously at $t equals 0 comma$ a small pebble is projected with speed $v$ frompoint $P$ is at angle of $45 degree$ as shown in the figure. Point $P$ is at a horizontal distance of $10 blank m$ from $O.$ If the pebble hits the block at $t equals 1 s comma$ the value of $v$ is (take $g equals 10 m divided by s to the power of 2 end exponent$ )

A small block is connected to one end of a massless spring of un-stretched length $4.9 m$ . The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by $0.2 m$ and released from rest at $t equals 0.$ It then executes simple harmonic motion with angular frequency $omega equals fraction numerator pi over denominator 3 end fraction r a d divided by s.$ Simultaneously at $t equals 0 comma$ a small pebble is projected with speed $v$ frompoint $P$ is at angle of $45 degree$ as shown in the figure. Point $P$ is at a horizontal distance of $10 blank m$ from $O.$ If the pebble hits the block at $t equals 1 s comma$ the value of $v$ is (take $g equals 10 m divided by s to the power of 2 end exponent$ )

physics-General

A projectile of mass m is fired with velocity v from a point P as shown. Neglecting air resistance, the magnitude of the changed in momentum between the points P and arriving at Q is

A projectile of mass m is fired with velocity v from a point P as shown. Neglecting air resistance, the magnitude of the changed in momentum between the points P and arriving at Q is

physics-General

Blocks A and B of equal masses are arranged as shown in figure. The surface of A is smooth while B is rough and has a coefficient of friction 0.1 with surface. The block A moves with speed 10 m/s and collides with B. The collision is perfectly elastic. Find the distance moved by B before it comes to rest.

Blocks A and B of equal masses are arranged as shown in figure. The surface of A is smooth while B is rough and has a coefficient of friction 0.1 with surface. The block A moves with speed 10 m/s and collides with B. The collision is perfectly elastic. Find the distance moved by B before it comes to rest.

physics-General

parallel

A ball moving with velocity u collides with two identical balls placed in the track of first ball, after the elastic collision,

A ball moving with velocity u collides with two identical balls placed in the track of first ball, after the elastic collision,

physics-General

Ball 1 collides with another identical ball 2 at rest as shown in figure. For what value of coefficient of restitution e, the velocity of second ball becomes two times that of 1 after collision

Ball 1 collides with another identical ball 2 at rest as shown in figure. For what value of coefficient of restitution e, the velocity of second ball becomes two times that of 1 after collision

physics-General

A bullet of mass 20 g travelling horizontally with a speed of 500 m/s passes through a wooden block of mass 10.0 kg initially at rest on a surface. The bullet emerges with a speed of 100 m/s and the block slides 20 cm on the surface before coming to rest, the coefficient of friction between the block and the surface. $(g = 10 m / s^{2})$

A bullet of mass 20 g travelling horizontally with a speed of 500 m/s passes through a wooden block of mass 10.0 kg initially at rest on a surface. The bullet emerges with a speed of 100 m/s and the block slides 20 cm on the surface before coming to rest, the coefficient of friction between the block and the surface. $(g = 10 m / s^{2})$

physics-General

parallel

Let f : R → R be a function defined by f(x) = $\frac{e^{\cos x} - e^{- \sin x}}{e^{\sin x} + e^{- \sin x}}$ , then

Let f : R → R be a function defined by f(x) = $\frac{e^{\cos x} - e^{- \sin x}}{e^{\sin x} + e^{- \sin x}}$ , then

The variation of potential energy of harmonic oscillator is as shown in figure. The spring constant is

The variation of potential energy of harmonic oscillator is as shown in figure. The spring constant is

physics-General

As shown in figure, a simple harmonic motion oscillator having identical four springs has time period

As shown in figure, a simple harmonic motion oscillator having identical four springs has time period

physics-General

parallel

A man having a wrist watch and a pendulum clock rises on a $T V$ tower. The wrist watch and pendulum clock by chance fall from the top of the tower. Then

A man having a wrist watch and a pendulum clock rises on a $T V$ tower. The wrist watch and pendulum clock by chance fall from the top of the tower. Then

physics-General

A metal rod of length $L$ and mass $m$ is pivoted at one end. A thin disk of mass $M$ and radius $R left parenthesis less than L right parenthesis$ is attached at its centre to the free end of the rod. Consider two ways the disc is attached case $A$ - the disc is not free to rotate about its centre and case $B$ – the disc is free to rotate about its centre. The rod-disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is/are true?

A metal rod of length $L$ and mass $m$ is pivoted at one end. A thin disk of mass $M$ and radius $R left parenthesis less than L right parenthesis$ is attached at its centre to the free end of the rod. Consider two ways the disc is attached case $A$ - the disc is not free to rotate about its centre and case $B$ – the disc is free to rotate about its centre. The rod-disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is/are true?

physics-General

Let f: R → R be a function defined by f(x) = – $fraction numerator vertical line x vertical line to the power of 3 end exponent plus vertical line x vertical line over denominator 1 plus x to the power of 2 end exponent end fraction$ , then the graph of f(x) lies in the –

Let f: R → R be a function defined by f(x) = – $fraction numerator vertical line x vertical line to the power of 3 end exponent plus vertical line x vertical line over denominator 1 plus x to the power of 2 end exponent end fraction$ , then the graph of f(x) lies in the –

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.