Introduction to Radial & Tangential Acceleration

Q. The value of Gravitional cons†an t in MKS system is 6.67×10^{-11 }N-m^2/kg^2. What will be its value in CGS system

Q.

A body is revolving with a constant speed along a circle. If its direction of motion is reversed but the speed remains the same, then which of the following statement is true

1. The centripetal force will not suffer any change in magnitude

2. The centripetal force will have its direction reversed

3. The centripetal force will not suffer any change in direction

4. The centripetal force would be doubled

Q. A body moving in a circular path with a constant speed has a ________

1. constant velocity

2. constant kinetic energy

3. constant acceleration

4. constant momentum

Q.

A simple pendulum of length L having a bob of mass m is deflected from its rest position by an angle $\theta$ and released (figure) The string hits a peg which is fixed at a distance x below the point of suspension and the bob starts going in a circle centred at the peg. If the pendulum is released with $\theta ={90}^{\circ }$ and x = $\frac{L}{2}$ find the maximum height reached by the bob above its lowest position before the string becomes slack.

1. None of these

2. 

3. 

4. 

Q.

An earth satellite of mass m revolves in a circular orbit at a height h from the surface of the earth. R is the radius of the earth and g is acceleration due to gravity at the surface of the earth. The velocity of the satellite in the orbit is given by

1. 

2. gR

3. 

4. 

Q. A disc of mass m and radius R is rolling without slipping as shown. The magnitude of net velocity of the point P is ( OP = R/2 )

Q. what is the relation between centripetal force and and gravitation.

Q. an ideal spring is used to fire a 2 g block horizontally across a frictionless table top . the spring has spring cons†an 80 N/m and is initially compressed by 3 cm . the speed of the block as it leaves the spring is

Q.

A flat plate is separated from a large plate by a layer of glycerine of thickness 3 X 10^-3m. If the co-efficient of viscocity of glycerine is 2 Nsm², what is the force required to keep the plate moving with a velocity of 6 X 10^-2 m/s. Area of the plate is 4.8 X 10^-3m².

1. 19.2 N

2. 1.92 N

3. 0.192 N

4. 192 N

Q.

A block of mass m is kept on a horizontal ruler. The friction coefficient between the ruler and the block is μ. The ruler is fixed at one end and the block is at a distance L from the fixed end. The ruler is rotated about the fixed end in the horizontal plane through the fixed end. If the angular speed of the ruler is uniformly increased from zero at an angular acceleration α, at what angular speed will the block slip?

1. 

2. 

3. 

4. None of these

Q.

A stone of mass 1 kg tied to a light inextensible string of length $L=\frac{10}{3}m$ is whirling in a circular path of radius $L$ in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is 4 and if g is taken to be $10m/se{c}^2$ , the speed of the stone at the highest point of the circle is

1. 

2. 

3. 

4. 

Q. Relation between Angular ve Linear velocity and Linearvelocity.

Q. 39.Calculate the gravitational force of attraction between a woman weighing 50 kg and and her child of 12 kg seperated by a distance of 2m.

Q. A point moves along a circle of radius $4\text{m}$. The distance $x$ is related to time by $x=c{t}^3$. What should be the value of $c$, so that the tangential acceleration is equal to the normal acceleration when its linear velocity is $4\text{m/s}$?

1. $0.288{\text{m/s}}^2$
2. $0.288{\text{m/s}}^3$
3. $0.333{\text{m/s}}^2$
4. $0.333{\text{m/s}}^3$

Q. Wheel A of radius $r_A=10\text{cm}$ is coupled by belt B to a wheel C of radius $r_c=25\text{cm}$. The angular speed of the wheel A is increased from rest at a constant rate of $1.6{\text{rad/s}}^2.$ Find the time needed for wheel C to reach an angular speed of $100\text{rev/min},$ assuming that the belt does not slip.

1. 4 seconds
2. 9 seconds
3. 16 seconds
4. 25 seconds

Q. A cylinder having radius 0.4 m, initially rotating at t=0 with initial angular velocity equal to 54 rad per second is placed on a rough inclined plane with inclination angle equal to 37° with friction coefficient equal to 0.5. The time taken by cylinder to start pure rolling is( take g= 10m/s^2).

Q.

At t₁ = 2.00 s, the acceleration of a particle in counter clockwise circular motion is It moves at constant speed. At time t₂ = 5.00 s, the particle's acceleration is What is the radius of the path taken by the particle if t₂ - t₁ is less than one period?

1. $\frac{40}{{\pi }^2}$

2. $\frac{360}{{\pi }^2}$
3. $\frac{30}{{\pi }^2}$
4. $\frac{60}{{\pi }^2}$

Q.

A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t₁ = 5.00 s, it is at point (5.00 m, 6.00 m) with velocity (3π m/s)$\hat{j}$ and acceleration in the positive x direction. At time t₂ = 10.0 s, it has velocity (-3π m/s)$\hat{i}$​ and acceleration in the positive y direction. What are the (a) x and (b) y coordinates of the center of the circular path if t₂ - t₁ is less than one period?

1. (15 m, 6 m)

2. (-5 m, 6)

3. (15 m, 0)

4. (-5 m, 0)

Q. a particle moves in a straight line, so that x=root t then its acceleration is proportional to

Q. The tangential acceleration of a particle in a circular motion of radius $2\text{m}$ is $a_t=\alpha t{\text{m/s}}^2$ (where $\alpha$ is a constant) . Initially, the particle is at rest. Net acceleration vector of the particle makes ${45}^{\circ }$ with the radial acceleration after 2 sec. The value of constant $\alpha$ is:

1. $\frac{1}{2}{\text{m/s}}^3$
2. $1{\text{m/s}}^3$
3. $2{\text{m/s}}^2$
4. $1{\text{m/s}}^2$

Q.

A cyclist bends while taking a sharp turn so that

1. it looks nice

2. component of his weight provides centripetal force

3. he can go fast

4. friction is reduced

Q. A coin is pushed down tangentially from an angular position $\theta$ on a circular surface, with velocity $v$ as shown. If the cofficient of friction between the coin and surface is $\mu$, find the tangential acceleration of the coin.

1. $g\sin \theta$
2. $g\sin \theta -\mu g\cos \theta$
3. $g\sin \theta -\mu g\cos \theta -\mu v^2/R$
4. $g\sin \theta -\mu v^2/R$

Q. A cylinder having radius 0.4m, initially rotating at t=0 with initial angular velocity equal to 54rad/sec is placed on a rough inclined plane inclined at 37 degree with horizontal and friction coefficient is 0.5. The time taken by the cylinder to start pure rolling is g=10m/s^2.

Q. A small block is placed on a turn table. The coefficient of static friction between the block and the table is ${\mu }_s=0.5$. If the turn table is rotating with constant angular acceleration $\alpha =3{\text{rad/s}}^2$, what will be the angular speed at which the block begins to slip on the table ?
Given $r=1\text{m},g=10{\text{m/s}}^2.$

1. $1\text{rad/s}$
2. $2\text{rad/s}$
3. $3\text{rad/s}$
4. $4\text{rad/s}$

Q. A particle moves in a circle of radius $3.5\text{cm}$ at a speed given by $v=8t$, where $v$ is in $\text{cm/s}$ and $t$ in seconds. Find the tangential acceleration at $t=2\text{s}$. (in ${\text{cm/s}}^2)$

1. $32{\text{cm/s}}^2$
2. $24{\text{cm/s}}^2$
3. $16{\text{cm/s}}^2$
4. $8{\text{cm/s}}^2$

Q. A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its net acceleration vector $\overrightarrow{a}$ is correctly shown in which of the following options ?

1. 
2. 
3. 
4. 

Q.

A particle moves in a circle of radius 2.0 cm at a speed given by v = 4t, where v is in cm/s and t is in seconds.
Find the tangential acceleration at t =1 s.
Find total acceleration at t =1 s.

1. Tangential acceleration $=2cm/s^2$
   Total acceleration $=4\sqrt{5}cm/s^2$

2. Tangential acceleration $=4cm/s^2$
   Radial acceleration $=4\sqrt{5}cm/s^2$

3. Tangential acceleration $=2cm/s^2$
   Radial acceleration $=8cm/s^2$

4. Tangential acceleration $=4cm/s^2$
   Radial acceleration $=16cm/s^2$

Q.

If r represents the radius of the orbit of a satellite of mass m moving around a planet of mass M, the velocity of the satellite is given by

1. 

2. 

3. 

4. 

Q. A car of mass $m$ is moving on a horizontal circular track of radius $r$. The time taken to finish one complete revolution is $\frac{\pi }{2}\text{s}$. If the velocity of the car at an instant $t$ is given by $v=5\sin 2t$, then the magnitude of tangential acceleration of the car at the time when it finishes a quarter circle is $p$. The value of $p^2$ is (No slipping between the car and track)

Q. Angular velocity of a particle is $\omega =\frac{{\theta }^2}{2}$, where $\theta$ is angular position of particle. Tangential acceleration of particle when it has covered $1$ revolution in a circle of radius $2\text{m}$ is

1. $4{\pi }^3$
2. $8{\pi }^3$
3. $2{\pi }^3$
4. $16{\pi }^3$