Q5. A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time $t$. Which of the following curve best describes acceleration of the block with time:
(1) [Figure]
(2) [Figure]
(3) [Figure]
(4) [Figure]

Q5. A 90 kg body placed at 2 R distance from surface of earth experiences gravitational pull of : ( $\mathrm { R } =$ Radius of earth, $\mathrm { g } = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ )
(1) 100 N
(2) 300 N
(3) 225 N
(4) 120 N

Q5. When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be:
(1) $6 \%$
(2) $600 \%$
(3) $60 \%$
(4) $500 \%$

Q5. Three bodies A , B and C have equal kinetic energies and their masses are 400 g .1 .2 kg and 1.6 kg respectively. The ratio of their linear momenta is :
(1) $\sqrt { 2 } ; \sqrt { 3 } ; 1$
(2) $1 : \sqrt { 3 } : 2$
(3) $1 : \sqrt { 3 } : \sqrt { 2 }$
(4) $\sqrt { 3 } : \sqrt { 2 } : 1$

Q5. The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:
(1) $1 : 9$
(2) $1 : 3$
(3) $1 : 27$
(4) $1 : 81$

Q6. If a rubber ball falls from a height $h$ and rebounds upto the height of $h / 2$. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are :
(1) $50 \% , \sqrt { 2 \mathrm { gh } }$
(2) $50 \% , \sqrt { \mathrm { gh } }$
(3) $40 \% , \sqrt { 2 \mathrm { gh } }$
(4) $50 \% , \sqrt { \frac { \mathrm { gh } } { 2 } }$

Q6. Correct formula for height of a satellite from earths surface is:
(1) $\left( \frac { T ^ { 2 } R ^ { 2 } } { 4 \pi ^ { 2 } g } \right) ^ { 1 / 3 } - R$
(2) $\left( \frac { T ^ { 2 } R ^ { 2 } g } { 4 \pi ^ { 2 } } \right) ^ { 1 / 3 } - R$
(3) $\left( \frac { T ^ { 2 } R ^ { 2 } g } { 4 \pi ^ { 2 } } \right) ^ { - 1 / 3 } + R$
(4) $\left( \frac { T ^ { 2 } R ^ { 2 } g } { 4 \pi } \right) ^ { 1 / 2 } - R$

Q6. Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis AB as shown in figure is $\sqrt { 8 / x }$. The value of $x$ is : [Figure]
(1) 51
(2) 34
(3) 17
(4) 67

Q6. Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?
(1) 75 N
(2) 300 N
(3) 375 N
(4) 225 N

Q6. Two satellite $A$ and $B$ go round a planet in circular orbits having radii $4 R$ and $R$ respectively. If the speed of A is $3 v$, the speed of B will be :
(1) $3 v$
(2) $6 v$
(3) $\frac { 4 } { 3 } v$
(4) $12 v$

Q6. A spherical ball of radius $1 \times 10 ^ { - 4 } \mathrm {~m}$ and density $10 ^ { 5 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$ falls freely under gravity through a distance $h$ before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of $h$ is approximately: (The coefficient of viscosity of water is $9.8 \times 10 ^ { - 6 } \mathrm {~N} \mathrm {~s} / \mathrm { m } ^ { 2 }$ )
(1) 2296 m
(2) 2518 m
(3) 2249 m
(4) 2396 m

Q7. A metal wire of uniform mass density having length $L$ and mass $M$ is bent to form a semicircular arc and a particle of mass $m$ is placed at the centre of the arc. The gravitational force on the particle by the wire is :
(1) $\frac { \mathrm { GmM } \pi ^ { 2 } } { \mathrm {~L} ^ { 2 } }$
(2) $\frac { \mathrm { GMm } \pi } { 2 \mathrm {~L} ^ { 2 } }$
(3) 0
(4) $\frac { 2 \mathrm { GmM } \pi } { \mathrm { L } ^ { 2 } }$

Q7. Given below are two statements : Statement I : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well. Statement II : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube. In the light of the above statements, choose the correct answer from the options given below:
(1) Statement I is true but Statement II is false.
(2) Statement I is false but Statement II is true.
(3) Both Statement I and Statement II are false.
(4) Both Statement I and Statement II are true.

Q7. A simple pendulum doing small oscillations at a place R height above earth surface has time period of $T _ { 1 } = 4 \mathrm {~s}$. $T _ { 2 }$ would be it's time period if it is brought to a point which is at a height 2 R from earth surface. Choose the correct relation [ $R =$ radius of earth] :
(1) $2 \mathrm {~T} _ { 1 } = \mathrm { T } _ { 2 }$
(2) $2 \mathrm {~T} _ { 1 } = 3 \mathrm {~T} _ { 2 }$
(3) $\mathrm { T } _ { 1 } = \mathrm { T } _ { 2 }$
(4) $3 \mathrm {~T} _ { 1 } = 2 \mathrm {~T} _ { 2 }$

Q7. Match List-I with List-II :

	List-I		List-II
(A)	A force that restores an elastic body of unit area to its original state	(I)	Bulk modulus
(B)	Two equal and opposite forces parallel to opposite faces	(II)	Young's modulus
(C)	Forces perpendicular everywhere to the surface per unit area same everywhere	(III)	Stress
(D)	Two equal and opposite forces perpendicular to opposite faces	(IV)	Shear modulus

Choose the correct answer from the options given below :
(1) (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
(2) (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
(3) (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
(4) (A)-(III), (B)-(I), (C)-(II), (D)-(IV)

Q7. Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : $R =$ Radius of bubble S = Surface tension of bubble)
(1) $\frac { 2 S } { R }$
(2) $\frac { 4 R } { S }$
(3) $\frac { S } { R }$
(4) $\frac { 4 S } { R }$

Q7. A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil $= 0.8$, specific gravity of ice $= 0.9$ ) [Figure]
(1) $1 : 1$
(2) $5 : 4$
(3) $8 : 9$
(4) $9 : 10$

Q7. A sphere of relative density $\sigma$ and diameter $D$ has concentric cavity of diameter $d$. The ratio of $\frac { D } { d }$, if it just floats on water in a tank is :
(1) $\left( \frac { \sigma - 2 } { \sigma + 2 } \right) ^ { 1 / 3 }$
(2) $\left( \frac { \sigma } { \sigma - 1 } \right) ^ { 1 / 3 }$
(3) $\left( \frac { \sigma - 1 } { \sigma } \right) ^ { 1 / 3 }$
(4) $\left( \frac { \sigma + 1 } { \sigma - 1 } \right) ^ { 1 / 3 }$

Q7. A real gas within a closed chamber at $27 ^ { \circ } \mathrm { C }$ undergoes the cyclic process as shown in figure. The gas obeys $P V ^ { 3 } = R T$ equation for the path $A$ to $B$. The net work done in the complete cycle is (assuming $R = 8 \mathrm {~J} / \mathrm { molK }$ [Figure] ):
(1) 20 J
(2) 205 J
(3) - 20 J
(4) 225 J

Q8. Given below are two statements: Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $P _ { 1 } - P _ { 2 } = \rho g \left( h _ { 2 } - h _ { 1 } \right)$. Statement II : In ventury tube shown $2 \mathrm { gh } = v _ { 1 } ^ { 2 } - v _ { 2 } ^ { 2 }$ [Figure]
In the light of the above statements, choose the most appropriate answer from the options given below.
(1) Both Statement I and Statement II are correct.
(2) Statement I is correct but Statement II is incorrect.
(3) Statement I is incorrect but Statement II is
(4) Both Statement I and Statement II are incorrect. correct.

Q8. A sample of gas at temperature $T$ is adiabatically expanded to double its volume. Adiabatic constant for the gas is $\gamma = 3 / 2$. The work done by the gas in the process is: ( $\mu = 1$ mole)
(1) $R T [ 1 - 2 \sqrt { 2 } ]$
(2) $R T [ \sqrt { 2 } - 2 ]$
(3) $R T [ 2 - \sqrt { 2 } ]$
(4) $R T [ 2 \sqrt { 2 } - 1 ]$

Q8. In hydrogen like system the ratio of coul0mbian force and gravitational force between an electron and a proton is in the order of :
(1) $10 ^ { 39 }$
(2) $10 ^ { 29 }$
(3) $10 ^ { 19 }$
(4) $10 ^ { 36 }$

Q8. During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $\frac { C _ { \mathrm { P } } } { C _ { \mathrm { v } } }$ for the gas is :
(1) $\frac { 5 } { 3 }$
(2) $\frac { 9 } { 7 }$
(3) $\frac { 3 } { 2 }$
(4) $\frac { 7 } { 5 }$

Q8. A total of 48 J heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by $2 ^ { \circ } \mathrm { C }$. The work done by the gas is: Given, $\mathrm { R } = 8.3 \mathrm {~J} \mathrm {~K} ^ { - 1 } \mathrm {~mol} ^ { - 1 }$.
(1) 24.9 J
(2) 72.9 J
(3) 48 J
(4) 23.1 J

Q8. Correct Bernoulli's equation is (symbols have their usual meaning) :
(1) $P + m g h + \frac { 1 } { 2 } m v ^ { 2 } =$ constant
(2) $P + \rho g h + \frac { 1 } { 2 } \rho v ^ { 2 } =$ constant
(3) $P + \rho g h + \rho v ^ { 2 } =$ constant
(4) $P + \frac { 1 } { 2 } \rho g h + \frac { 1 } { 2 } \rho v ^ { 2 } =$ constant