6. Two points of a rod move with velocity $3 v$ and $v$ along opposite direction seperated by a distantce ' $r$ . Calculate the angular velocitry of the rod w.r.t. its end.
12.0 DYNAMICS OF CIRCULAR MOTON
Velocity vector points always tangent to the path and continuously change its direction, as a particle moves on a circular path even with constant speed and give rise to normal component of acceleration, which always points toward the center of the circular path. This component of acceleration is known as centripetal (center seeking) acceleration and denoted by $a_{c} \cdot$ Moreover, if speed also changes the particle will have an additional acceleration component along the tangent to the path. This component of acceleration is
The centripetal and

Topic:

Work, Energy and Power

View solution

Question 27

Dynamics of Circular Motion and Banking of Roads 1. The whole set up shown in the figure is rotating with constant angular velocity ๑ on a horizontal frictionless table then the ratio of tensions

\frac{T _{1}}{T _{2}}

is (Given

\frac{ℓ _{2}}{ℓ _{1}} = \frac{2}{1}

)

$\frac{m _{1}}{m _{2}}$
$\frac{( m _{1} + 2 m _{2} )}{2 m _{2}}$
$\frac{m _{2}}{m _{1}}$
$\frac{( m _{2} + m _{1} )}{m _{2}}$

Topic:

Work, Energy and Power

View 2 solutions

Question 28

A vehicle can travel round a curve at a higher speed when the road is banked than when the road is level. This is because

banking increases the coefficient of friction
banking increases the radius,
the normal reaction has a horizontal component,
when the track is banked the weight of the car acts down the incline.

Topic:

Work, Energy and Power

View solution

Question 29

Work Power Ene Dynamics of Circular Motion and Banking of Roads 1. The whole set up shown in the figure is rotating with constant angular velocity

$\frac{m _{1}}{m _{2}}$
$\frac{m _{2}}{m _{1}}$
$\frac{( m _{1} + 2 m _{2} )}{2 m _{2}}$
$\frac{( m _{2} + m _{1} )}{m _{2}}$

Topic:

Work, Energy and Power

View solution

Question 30

Example 9 A pendulum is pulled to one side until its bob is

10 cm

higher than when weighing vertically and is then released as shown in Fig. 6.2. What is its speed as it passes through the mid-point of swing?

Topic:

Work, Energy and Power

View solution

Found the solution, but did not understand the concept?

Connect with a tutor in less than 60 seconds 24x7

Ask my first question

Question 31

(Take

g = 10 m / s^{2}

) 6. A car is travelling at

30 km / h

in a circle of radius

60 m

. What is the minimum value of

μ_{s}

for the car to make the turn without skidding ? 7. A stone of mass

0.25 kg

tied to the end of a string is whirled round in a circle of radius

1.5 m

with

a

spowi of

40 rev / min

in horizontal plane. What is the tension in string? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of

200 N

Topic:

Work, Energy and Power

View solution

Question 32

T_{1}, T_{2}

and

T_{3}

are tensions in the three strings. Then

T_{1} : T_{2}

-

$3 : 2$
$3 : 1$
$2 : 1$
$1 : 2$

Topic:

Work, Energy and Power

View 2 solutions

Question 33

l

is describing a vertical circle and its speed at the bottommost point is

7 g l

. Then its speed at the topmost point will be- (a)

g l

(b)

2 g l

(c)

3 g l

(d)

5 g l .8

. The acceleration due to gravity at a height

R

(radius of the

Topic:

Work, Energy and Power

View solution

Question 34

of a particle are

m, 1

is - (a)

\frac{p ^{2}}{2 m}

(b)

\frac{p v}{2 m}

(c)

\frac{p m}{2}

(d)

\frac{p ^{2}}{2 v} 7

. A particle tied to a bottommost point is

7 g!

. lis describing a vertical circle and its speed at the bett

g l

(b)

2 g l

(c)

3 g l

(d)

5 g l .8

. The acceleration due earth) from the earth's surface is - (a)

\frac{g}{2}

(b)

\frac{g}{3}

(c)

\frac{g}{4}

(d)

\frac{g}{16}, 9

. A spring earth) from the earth's surface is- (a) of spring constant

k

is cut into two identical

^{2}

. A cylinder contains a liquid

Topic:

Work, Energy and Power

View solution

Question 35

Then its speed at the topmost point will be- (a)

g l

(b)

2 g l

(c)

3 g l

(d)

5 g l

.8. The acceleration due to gravity at a height

R

(radius of the earth) from the earth's surface is - (a)

\frac{g}{2}

(b)

\frac{R}{3}

(c)

\frac{g}{4}

(d)

\frac{g}{16}, 9

. A spring f cnring constant

k

is cut into two identical pieces. Then spring constant

Topic:

Work, Energy and Power

View solution

Question 36

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that [AIEEE 2004]

Its velocity is constant
Its acceleration is constant
Its kinetic energy is constant
It moves in a straight line

Topic:

Work, Energy and Power

View 3 solutions

Question 37

of radiation of maximum intensity will be (a)

λ

(b)

2 λ

(c)

\frac{λ}{2}

(d)

4 λ .12

. A Carnot engine absorbs 40 cal heat from source having temperature

320 K

and rejects

30 cal

heat to sink. The temperature of the sink is - (a)

200 K

(b)

270 K

(c)

240 K

(d)

300 K .13

. The equation of an S. H. M. is

x = 8 sin

Topic:

Work, Energy and Power

View solution

Question 38

\[ \begin{array}{l} m_{1} v_{2}+m_{2} v_{2}=m_{1} u_{1}+m_{2} u_{2}+m_{1} u_{1}-m_{1} u_{2} \\ \left(m_{1}+m_{2}\right) v_{2}=\left(m_{2}-m_{1}\right) u_{2}+2 m_{1} u_{1} \\ \therefore v_{2}=\left[\frac{2 m_{1}}{m_{1}+m_{2}}\right] u_{1}+\left[\frac{m_{2}-m_{1}}{m_{1}+m_{2}}\right] u_{2} \end{array} \] This is the equation for final velocity of the second body after the collision. State and prove law of conservation of energy in case of freely falling body. Law of conservation of energy: The total mechanical energy of a system is co forces doing work on it are conservative. Law of conservation energy in case of freely falling body:

Topic:

Work, Energy and Power

View solution

Question 39

A bob of mass '

m

' is released from angle

θ

with vertical as shown in figure. Find the workdone by gravity when pendulum stop vibrating.

$m gL$
$m gL cos θ^{\circ}$ .
$m gL sin θ$
$m gL (1 - cos θ)$

Topic:

Work, Energy and Power

View 2 solutions

Question 40

the arge amount of power loss in engines.

Polishing : When surfaces are pollshed, friction (Mar- 09,14, May-0 decreases.
Ball-Bearings : The hard steel balls(called bearing) placed betweer friction into rolling friction hence friction is reduced.
Lubricants : Lubricants like oil (or) grease which spreads over the surface thereby the friction is reduced.
Streamlining : By making front portion of vehides in a curved shape State the laws of rolling friction.

Topic:

Work, Energy and Power

View solution