Laws of Motions (Question Paper)

ANDHERI / BORIVALI / DADAR / CHEMBUR / THANE / MULUND/ NERUL / POWAI

IIT-JEE 2014

TW TEST

TIME: 1 ½ HRS

MARKS: 65

TOPICS: LAWS O MOTION

DATE:

3 N 2

1

1. Two blo block ckss of of mas masse sess 2 kg kg and and 1 kg kg are are in in con conta tact ct with with each each othe otherr on on a frictionless table. When a horizontal force of 3.0 N is applied to the block of mass 2 kg, the vale of  the force of contact between two blocks is! "a# $ N "b# 3 N "c# 2 N "d# 1 N 2.

%n the the fig figre re give given n bel below ow,, wha whatt is the the read readin ing g of of the the bala balanc nce& e&

kg −1 "Take g ' 10 N "a# 10 N 3.

# "b# 20 N

"c# ( N

"d# zero

Three hree blo blocks cks of of mas masse sess 2 kg, kg, 3 kg kg and and ( kg kg are are co connec nnecte ted d to to each other with light string and are then placed on a smooth frictionless srface. The s)stem is plled with a force * from the the side side of the the ligh lighte terr mass ass so that that is moves oves with with an

T2 s −2 T1 acceleration of 1 m . and  denotes the tensions in the other strings. The vale of * is! "a# 2 N "b# 3 N "c# ( N "d# 10 N s $.

The The elev elevat ator or sho shown wn in in the the fig figre re is is desc descen endi ding ng,, with with an an acce accele lera rati tion on of of 2 m . The mass of the block + ' 0.( kg. The force eerted eer ted b) the block + on the block - is! 10m s

2

"Take g '

#

"a# 2 N (.

−2

"b# $ N

"c#  N

"d# / N

Two mas masse sess of / kg kg and and $ kg kg are are conn connec ecte ted d b) a str strin ing g as sho shown wn in in the the figre over a frictionless plle). The acceleration of the s)stem is!

2 m s −2

$ m s −2 "a#

"b#

./ms −2 "c#zero

H!"# O$$%&!: A'#(!)%

"d#

:

2624522*

MUMBAI / DELHI/ AKOLA / KOLKATA KOLKATA / LUCKNOW

.

Two bodies of mass $ kg and kg are attached to the ends of a massless, inetensible string passing over a fied and smooth plle). The $ kg mass is attached to the table

T1 top b) another string. The tension in this string g = 10 m s

is eal to

2

"Take "a# 20 N

H!"# O$$%&!: A'#(!)%

# "b# 2( N

:

2624522*

"c# 10. N

"d# 10 N

MUMBAI / DELHI/ AKOLA / KOLKATA / LUCKNOW

 1 .

Three forces are acting on a particle of mass m initiall) in eilibrim. %f the first 2 forces "

(  3 )

 2 # are perpendiclar to each other and sddenl) the third force acceleration of the particle is  3  1 +  2  1 −  2

m

m

"a# /.

is removed, then the

 1

m

"b#

m

"c#

"d#

+ plmb bob is hng from the ceiling of a train compartment. The train moves on an inclined track

a =g 2

30 o

of inclination with horizontal. +cceleration of train p the plane is string spporting the bob makes with normal to the ceiling in eilibrim is

(

tan −1 2

30 o "a# .

and

3

)

tan −1

"b#

(

3 2

)

"c#

. The angle which the

tan −1 ( 2 ) "d#

+ssming that the block - alwa)s remains horizontal, hence the acceleration of - is

 m s2

2 m s2

"a#

"b#

$ m s2 "c# 10.

"d# none of these

+s shown in the fig., if acceleration of 4 with respect to grond

( m s2 is

, then

( m s2 "a# +cceleration of m with respect to 4 is

( m s2 "b# +cceleration of m with respect to grond is

2 m s2 "c# +cceleration of m with respect 4 is

10m s 2 "d# +cceleration of m with respect to grond is 11.

+ painter of mass 4 stands on a platform of mass m and  plls himself p b) two ropes which hang over plle) as shown in fig. 5e plls each rope with force * and moves pward with a niform acceleration a. *ind a neglecting the fact that no one cold do this for long time.

$* + ( 24 + m ) g

$* + ( 4 + m ) g

$* − ( 4 + m ) g

$* − ( 4 + m ) g

4 + 2m

4 + 2m

4+m

24 + m

"a#

H!"# O$$%&!: A'#(!)%

"b#

:

2624522*

"c#

"d#

MUMBAI / DELHI/ AKOLA / KOLKATA / LUCKNOW

12.

Two trolle) + and - are moving with accelerations a and 2a respectivel) in the same direction. To an observer in trolle) +, the magnitde of psedo force acting on a block of mass m on the trolle) - is "a# zero "b# ma "c# 2 ma "d# none

13.

6)stem is shown in the figre and man is plling the rope from both sides with constant speed 78. Then the velocit) of the block will be

1$.

3

3



$

2

$

"a# "b# "c# "d# none 6)stem is shown in figre and wedge is moving towards left with speed 2 m9s. Then velocit) of the block - will be

3 "a# m9s "c# 2 m9s 1(.

"b# 1 m9s "d# $ m9s

%n the figre shown, the speed of the trck is v to the right. The speed with

θ = 0 o which the block is moving p at "a# v

1.

"b# 2v93

 is! "c# 3v9$

"d# none

+ s)stem is shown in the figre. +ll speeds shown are with respect to grond. The speed of -lock + with respect to grond is ! "a# 20 m9s

"b# 2( m9s

"c# 1( m9s

"d# 10 m9s

1.

%n the figre if blocks + and - move with same horizontal acceleration de to eternal force applied on -, there is no friction between + and - , then the magnitde of interaction force between the two blocks will be ! "a# 2 mg 9 cos θ "b# 2 mg cos θ "c# mgcosθ "d# none of these

1/.

Two masses m1 and m2 which are connected with a light string are placed over a frictionless plle). This set p is placed over a weighing machine, as shown. Three combination of masses m 1 and m2 are sed, in first case m1 '  kg , and m 2 ' 2kg, in second case m 1 ' ( kg and m 2 ' 3 kg and in third case m1  ' $kg and m 2  ' $ kg. 4asses are held stationar) initiall) and then released. %f the readings of the weighing machine after the release in three cases are W1 , W2 and W3 respectivel) then! "a# W1:W2: W3 "b# W1; W2; W3 "c# W1 ' W2 ' W3 "d# W1 ' W2; W3

1.

-lock + of mass m is placed over a wedge - of same mass m. +ssming all srfaces to be smooth, the displacement of block + in 1 s if the s)stem is released from rest is

H!"# O$$%&!: A'#(!)%

:

2624522*

MUMBAI / DELHI/ AKOLA / KOLKATA / LUCKNOW

( 1 + sin θ ) g ( 1 − sin θ ) 2

gsin θ

2

2

"a#

"b# g

cos 2 θ

g

1 + sin 2 θ

"c#

sin 2 θ 1 + sin 2 θ

"d#

20.

*orce eerted b) the floor of a lift on the foot of a bo) standing on it is more than actal weight of the bo) if the lift is moving "a# down and speed is increasing "b# p and speed is increasing "c# p and speed is decreasing "d# down and speed is decreasing

21.

+ bod) of mass ( kg is

30 o

0o angles

sspended b) the strings making

and

with the

horizontal as shown in fig.

( g = 10 m s ) 2

T2 = 2(N

T1 = 2(N "a#

"b#

T2 = 2( 3N

T1 = 2( 3N "c#

"d#

22.

+ painter is appl)ing force himself to raise him and the bo with an acceleration of ( m9s2 b) a massless rope and plle) arrangement as shown in figre. 4ass of painter  is 100 kg and that of bo is (0 kg. %f g '10 m9s 2 , then ! "a# Tension in the rope is 112( N "b# Tension in the rope is 22(0 N "c# *orce of contact between the painter and the floor is 3( N "d# The pll force of the painter on the rope is frictional force

23.