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Physics-

General

Easy

Question

A semi cylindrical shell with negligible thickness oscillates without slipping on a horizontal surface.
The time period of small oscillations is (Hint : centre of mass of the shell lies at $fraction numerator 2 R over denominator pi end fraction$ below the centre)

$2 π \sqrt{\frac{R (π - 2)}{g}}$
$2 π \sqrt{\frac{R (π - 1)}{g}}$
$2 π \sqrt{\frac{R (π + 2)}{g}}$
$2 π \sqrt{\frac{R (π + 1)}{g}}$

The correct answer is: $2 pi square root of fraction numerator R left parenthesis pi minus 2 right parenthesis over denominator g end fraction end root$

Restoring torque = - mg (B(c) $I alpha equals negative m g open parentheses fraction numerator 2 R over denominator pi end fraction sin invisible function application theta close parentheses$

Related Questions to study

Initially spring is compressed by distance $x subscript 0 end subscript$ from equilibrium position. At this compression block is given velocity $square root of fraction numerator 3 k over denominator m end fraction end root x subscript 0 end subscript comma$ so that compression in the spring increases and block start SHM (Spring constant K). Equation of motion of the block is

Initially spring is compressed by distance $x subscript 0 end subscript$ from equilibrium position. At this compression block is given velocity $square root of fraction numerator 3 k over denominator m end fraction end root x subscript 0 end subscript comma$ so that compression in the spring increases and block start SHM (Spring constant K). Equation of motion of the block is

Physics-General

A ball is suspended by a thread of length l at the point O on the wall, forming a small angle $proportional to$ with the vertical (figure) Then the thread with the ball was deviated through 2 $proportional to$ and set free. Assuming the collision of the ball against the wall to be perfectly elastic, find the oscillation period of such a pendulum.

A ball is suspended by a thread of length l at the point O on the wall, forming a small angle $proportional to$ with the vertical (figure) Then the thread with the ball was deviated through 2 $proportional to$ and set free. Assuming the collision of the ball against the wall to be perfectly elastic, find the oscillation period of such a pendulum.

Physics-General

A mass m attached to a spring A has a frequency of 3 Hz and a spring B has a frequency of 4 Hz. When both the springs are connected as shown, find the frequency (in Hz) of oscillation.

A mass m attached to a spring A has a frequency of 3 Hz and a spring B has a frequency of 4 Hz. When both the springs are connected as shown, find the frequency (in Hz) of oscillation.

Physics-General

parallel

If we go deep into earth, time period of simple pendulum will:

If we go deep into earth, time period of simple pendulum will:

Physics-General

"The sky appears blue. This is due to atmospheric refraction.”
Identify whether the above statement is true or false.

"The sky appears blue. This is due to atmospheric refraction.”
Identify whether the above statement is true or false.

A car is moving with a speed of 100 kmh^-1 . if the mass of the car is 950 kg, then its kinetic energy is

A car is moving with a speed of 100 kmh^-1 . if the mass of the car is 950 kg, then its kinetic energy is

Physics-General

parallel

Acetic acid is a weak electrolyte because:

Acetic acid is a weak electrolyte because:

Chemistry-General

A body is projected horizontally from the top of a high tower with a speed of 20 m/s. After 4 sec the displacement of the body is (take g=10m/s²)

A body is projected horizontally from the top of a high tower with a speed of 20 m/s. After 4 sec the displacement of the body is (take g=10m/s²)

Physics-General

Consider the reaction: $blank C l subscript 2 end subscript left parenthesis a q right parenthesis plus H subscript 2 end subscript S left parenthesis a q right parenthesis ⟶ S left parenthesis s right parenthesis plus 2 H to the power of plus end exponent left parenthesis a q right parenthesis plus 2 C l to the power of minus end exponent left parenthesis a q right parenthesis$ The rate equation for this reaction is : $blank R a t e blank equals k open square brackets C l subscript 2 end subscript close square brackets open square brackets H subscript 2 end subscript S close square brackets$ Which of these mechanisms is/are consistent with this rate equation ?

Consider the reaction: $blank C l subscript 2 end subscript left parenthesis a q right parenthesis plus H subscript 2 end subscript S left parenthesis a q right parenthesis ⟶ S left parenthesis s right parenthesis plus 2 H to the power of plus end exponent left parenthesis a q right parenthesis plus 2 C l to the power of minus end exponent left parenthesis a q right parenthesis$ The rate equation for this reaction is : $blank R a t e blank equals k open square brackets C l subscript 2 end subscript close square brackets open square brackets H subscript 2 end subscript S close square brackets$ Which of these mechanisms is/are consistent with this rate equation ?

Chemistry-General

parallel

Two particles move in a uniform gravitational field with an acceleration g. At the initial moment the particles were located at one point and moved with velocities V₁ = 1 m/s and V₂ = 4 m/s horizontally in opposite directions. The distance between the particles at the moment when their velocity vectors become mutually perpendicular is (g=10m/s²)

Two particles move in a uniform gravitational field with an acceleration g. At the initial moment the particles were located at one point and moved with velocities V₁ = 1 m/s and V₂ = 4 m/s horizontally in opposite directions. The distance between the particles at the moment when their velocity vectors become mutually perpendicular is (g=10m/s²)

Physics-General

An endothermic reaction with high activation energy for the forward reaction is given by the diagram:

An endothermic reaction with high activation energy for the forward reaction is given by the diagram:

Chemistry-General

Graph between concentration of the product' x' and time' t' for $A rightwards arrow B$ is given ahead:
The graph between $negative fraction numerator d left square bracket A right square bracket over denominator d t end fraction$ and time wil1 be of the type:

Graph between concentration of the product' x' and time' t' for $A rightwards arrow B$ is given ahead:
The graph between $negative fraction numerator d left square bracket A right square bracket over denominator d t end fraction$ and time wil1 be of the type:

Chemistry-General

parallel

Following is the graph between $left parenthesis a minus x right parenthesis to the power of negative 1 end exponent$ and time t for second order reaction. $theta equals t a n to the power of negative 1 end exponent invisible function application left parenthesis 1 divided by 2 right parenthesis semicolon O A equals 2 L m o l to the power of negative 1 end exponent$ hence rate at the start of reaction will be:

Following is the graph between $left parenthesis a minus x right parenthesis to the power of negative 1 end exponent$ and time t for second order reaction. $theta equals t a n to the power of negative 1 end exponent invisible function application left parenthesis 1 divided by 2 right parenthesis semicolon O A equals 2 L m o l to the power of negative 1 end exponent$ hence rate at the start of reaction will be:

Chemistry-General

Following is the graph between log tll2 and log a (a = initial concentration) for a given
reaction at $27 to the power of ring operator end exponent$ e. Hence, order is:

Following is the graph between log tll2 and log a (a = initial concentration) for a given
reaction at $27 to the power of ring operator end exponent$ e. Hence, order is:

Chemistry-General

For the reaction $N H subscript 4 end subscript superscript plus end superscript plus O C N ⟶ N H subscript 2 end subscript C O N H subscript 2 end subscript$ the probable mechanism is,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell NH subscript 4 superscript plus plus OCN to the power of minus not stretchy rightwards harpoon over leftwards harpoon NH subscript 4 OCN end cell row cell text and end text space of 1em NH subscript 4 OCN not stretchy ⟶ NH subscript 2 CONH subscript 2 space of 1em text (slow) end text end cell end table$ The rate law will be:

For the reaction $N H subscript 4 end subscript superscript plus end superscript plus O C N ⟶ N H subscript 2 end subscript C O N H subscript 2 end subscript$ the probable mechanism is,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell NH subscript 4 superscript plus plus OCN to the power of minus not stretchy rightwards harpoon over leftwards harpoon NH subscript 4 OCN end cell row cell text and end text space of 1em NH subscript 4 OCN not stretchy ⟶ NH subscript 2 CONH subscript 2 space of 1em text (slow) end text end cell end table$ The rate law will be:

Chemistry-General

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