2018-10-01_Physics_For_You

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  1. A uniform rod of length l and mass m is swinging
    freely about a horizontal axis passing through its
    end. Its maximum angular speed is Z. Its centre of
    mass rises to a maximum height of


(a)

1


3


l^22
g

ω
(b)

1


6


l
g

ω

(c)

1


2


l^22
g

ω
(d)

1


6


l^22
g

ω


  1. The ratio of the radii of gyration of a circular disc and
    a circular ring of the same radii about a tangential
    axis is
    (a) 12: (b) 56: (c) 23: (d) 21:

  2. A solid sphere of uniform density and radius R
    applies a gravitational force of attraction F 1 on a
    particle placed at a distance 2R from the centre of
    the sphere. A spherical
    cavity of radius (R/2) is
    now made in the sphere
    as shown in gure. The
    sphere with cavity now
    applies a gravitational
    force F 2 on the same
    particle. The ratio (F 2 /
    F 1 ) is
    (a) 1/2 (b) 3/4 (c) 7/8 (d) 7/9

  3. A capillary tube is attached horizontally to a
    constant pressure head arrangement. If the radius
    of the tube is increased by 10%, the rate of ow of
    liquid will change nearly by
    (a) +10% (b) –10% (c) +46% (d) +40%

  4. Two rigid boxes containing dierent ideal gases
    are placed on a table. Box A contains one mole of
    nitrogen at temperature T 0 while box B contains
    one mole of helium at temperature (7/3)T 0. e
    boxes are then put into thermal contact with each
    other and heat ows between them until the gases
    reach a common nal temperature. (Ignore the heat
    capacity of boxes). Then the final temperature of
    the gases, Tf, in terms of T 0 , is


(a) TTf 5
2 0

(b) TTf

3


7 0


(c) TTf 7
3 0

(d) TTf 3
2 0


  1. Two vibrating tuning forks producing progressive
    waves given by y 1 = 4 sin (500pt) and y 2 = 2sin (506pt)
    are held near the ear of a person. The person will
    hear


O

R/2

R R

(a) 3 beats/s with intensity ratio between maxima
and minima equal to 2
(b) 3 beats/s with intensity ratio between maxima
and minima equal to 9
(c) 6 beats/s with intensity ratio between maxima
and minima equal to 2
(d) 6 beats/s with intensity ratio between maxima
and minima equal to 9


  1. If 2 moles of an ideal monoatomic gas at
    temperature T 0 is mixed with 4 moles of another
    ideal monoatomic gas at temperature 2T 0 , then the
    temperature of the mixture is
    (a) (5/3)T 0 (b) (3/2)T 0 (c) (4/3)T 0 (d) (5/4)T 0


SOLUTIONS


  1. (d) : Maximum acceleration = slope of BC


=

40


10


cms^1
s


= 4 cm s–2


  1. (b) : Height through which a body falls in t seconds,


(^) hg 1 t
2
(^2) ...(i)
Height through which the body falls in
(t – 2) seconds,
hg t


1


2


() (^22) ...(ii)
From eq (i) and (ii), we get
Thus, hh−′=−gt gt−=


1


2


1


2


(^22) () 240 m
or 2 g(t – 1) = 40 m
hence, t = 3 s (on putting g = 10 m s–2)
Clearly, h =


1


2


× (10) × (3)^2 m = 45 m


  1. (d) : At the highest point, vx 0 v^0
    2


and vy 0 = 0

Clearly, v 0 v^0
2

cos or q = 60°

R v
g

v
g

v
g

^0 vg

2
0

2
0

2
0

sins 2  in 120 (/ 32 ) () 322 /


  1. (a) : When the balloon descends with acceleration a,
    mg – F = ma ...(i)
    When the balloon ascends with acceleration a (with
    mass mc removed),
    F – (m – mc)g = (m – mc)a ...(ii)
    From eqns. (i) and (ii), we get
    (mg – ma) – mg + mcg = ma – mca
    or mc(g + a) = 2ma


or m

ma
ga

′=


+


2


()

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