Chapter 4 : Motion in a Plane

Q. Pick out the only vector quantity in the following list:

Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction, charge.

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Read each statement below carefully and state with reasons, if it is true or false :

(a) The magnitude of a vector is always a scalar,

(b) Each component of a vector is always a scalar,

(d) the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time,

(e) Three vectors not lying in a plane can never add up to give a null vector.

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Q. In a harbor, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbor flutters along the N-E direction. If the boat starts moving at as speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat ?

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Q. On an open ground, a motorist follows a track that turns to his left by an angle of

60^{o}

after every

500 m

. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.

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Read each statement below carefully and state, with reasons, if it is true or false :

(a) The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre.

(b) The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point.

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Rain is falling vertically with a speed of $30 m s^{- 1}$ . A woman rides a bicycle with a speed of $10 m s^{- 1}$ in the north to south direction. What is the direction in which she should hold her umbrella ?

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Q. Given

a + b + c + d = 0

, which of the following statements are correct.
(a)

a, b, c, d

must each be a null vector,
(b) The magnitude of (

a+c

) equals the magnitude of (

b + d

),
(c) The magnitude of

a

can never be greater than the sum of the magnitudes of

b, c

and

d

,
(d)

b + c

must lie in the plane of

a

and

d

a

and

d

are not collinear, and in the line of

a

and

d

, if they are collinear ?

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Q. A man can swim with a speed of

4.0 k m / h r

in still water. How long does he take to cross a river

1.0 k m

wide, if the river flows steadily at

3.0 k m / h r

and he makes his strokes normal to the river current? How far down the river does he go, when he reaches the other bank?

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Q. A cricketer can throw a ball to a maximum horizontal distance of

100 m

. How much high above the ground can the cricketer throw the same ball ?

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Q. A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the stone ?

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An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Compare its centripetal acceleration with the acceleration due to gravity.

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Q. The position of a particle is given by

r = 3.0 t^i - 2.0 t^{2}^j + 4.0^k m

where t is in seconds and the coefficients have the proper units for

r

to be in metres(a) Find the

v

and

a

of the particle?(b) What is the magnitude and direction of velocity of the particle at t = 2.0 s ?

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Q. Pick out the two scalar quantities in the following list :force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity.

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Q. State, for each of the following physical quantities, if it is a scalar or a vector: volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.

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Q. The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m/s can go without hitting the ceiling of the hall ?

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Q. Establish the following vector inequalities geometrically or otherwise :
(a)

|a+b| \leq |a| + |b|

(b)

|a+b| \geq ||a| - |b||

(c)

|a-b| \leq |a| + |b|

(d)

|a-b| \geq ||a| - |b||

When does the equality sign above apply?

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Q. Three girls skating on a circular ice ground of radius

200 m

start from a point

P

on the edge of the ground and reach a point

Q

diametrically opposite to

P

following different paths as shown in Fig. What is the magnitude of the displacement vector for each ? For which girl is this equal to the actual length of path skate ?

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A cyclist starts from the center O of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference, and returns to the center along QO as shown in Fig. If the round trip takes 10 min, what is the

(a) Net displacement,

(b) Average velocity, and

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A passenger arriving in a new town wishes to go from the station to a hotel located 10 km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. What is

(a) the average speed of the taxi.

(b) the magnitude of average velocity.

Are the two equal?

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Q. State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful :
(a) adding any two scalars, (b) adding a scalar to a vector of the same dimensions , (c) multiplying any vector by any scalar, (d) multiplying any two scalars, (e) adding any two vectors, (f) adding a component of a vector to the same vector.

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