IIT JEE Physics Test Paper 5

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IIT JEE Physics Test Paper 5

IIT JEE Physics Test Paper 5

1 Two blocks A & B with mass 4 kg and 6 kg respectively are connected by a stretched spring of negligible mass as in figure When the two blocks are released simultaneously the initial Smooth acceleration of B is 1.5 m/s2 westward. The acceleration of A is:

5-1

(A) 1m/s2 westward

(B)25 m/s2 eastward

(c)1 m/s2 eastward

(d)75 m/s2 westward

2. System shown in figure is in equilibrium and at rest. The spring and string are mass less Now the string is cut. The acceleration of mass 2 m and m just after the string is cut will be:

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(a) g/2 upwards, g downwards

(b) g upwards, g/2 downwards

(c) g upwards, 2g downwards

(d) 2g upwards, g downwards

3. The vertical displacement of block A in meter is given by y = t²/4 where t is in second. The downward acceleration of block B (in m/s²) is

5-3
(a) 4

(b) 8

(c) 10

(d) 5

4 A bead of mass m is located on a parabolic wire with its axis vertical and vertex directed towards downward as in figure and whose equation

is x² = ay. If the coefficient of friction is µ, the highest distance above
the x-axis at which the particle will be in equilibrium is

(a) µa (b) µ²a (c)1/4 µ^2 g (d)1/2µ^ g

5.In the shown arrangement if f1, f2 and T be the frictional forces on 2 kg block, 3 kg block & tension in the string respectively, then their values are:

(a) 2 N, 6 N, 3.2 N (b) 2 N, 6 N, 0 N
(c) 1 N, 6 N, 2 N (d) data insufficient to calculate the required values

6. The work done by the force F = A(y² ˆi + 2x²ˆj), where A is a constant and x & y are in meters around the path shown is:

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(a) zero

(b) A d

(c) A d²

(d) A d³

7. A ring of mass m can slide over a smooth vertical rod. The ring is connected to a spring of force constant

K = 4 mg /R 5-7

where 2R is the natural length of the spring. The other end of the spring is fixed to the ground
R

at a horizontal distance 2 R from the base of the rod. The mass is released at a height of

(a) work eone by the spring will be 3mgR / 2

(b) work eone by the spring will be 9mgR

(c) the velocity of the ring when it reaches the ground will be sqrt(gR)

(d) the velocity of the ring when it reaches the ground will be 2 sqrt(gR)

08. The given plot shows the variation of U, the potential energy of interaction between two particles with the distance separating them, r. Then which of the following statements are correct:

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(a) B and D are equilibrium points
(b) C is a point of unstable equilibrim
(c) The force of interaction between the two particles is attractive between points C and D and
repulsive between points D and E on the curve.
(d) The force of interaction between the particles is repulsive between point E and F on the curve.

09. A point P moves in counter-clockwise direction on a circular path as
shown in the figure. The movement of ‘P’ is such that it sweeps out a
length s = t³ + 5, where s is in metres and t is in seconds. The radius of
the path is 20 m. the acceleratino of ‘P’ when t = 2 s is nearly.

5-9

(a) 13 m/s²
(b) 12 m/s²
(c) 7.2 m/s²
(d) 14 m/s²

10. A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector a

5-10-A5-10-B5-10-C 5-10-D is correctly shown in

11. The centre of mass of the shaded portion of the disc. is: (The mass is uniformly distribusted in the shaded portion):

5-11

(a)R/20 to the left of A (b)R/12 to the left of A (c)R/20 to the right of A

(d)R/12 to the right of A

12. A ball of mass m strikes the fixed inclined plane after falling through a height h. If it rebounds elastically, the impulse on the ball is:

5-12

5-12-ans

13. Three particles of mass 20 g, 30 g and 40 g are initially moving along the positive direction of the
three coordinate axes respectively with the same velocity of 20 cm/s. If due to their mutual interaction,the first particle comes ot rest, the second acquires a velocity 10ˆi  20kˆ . What is then the velocity (in cm/s) of the third particle?
(a) 2ˆi +3ˆj + 4kˆ (b) 2.5ˆi + 15ˆj + 5kˆ (c) 2.5ˆi +10ˆj+ 5kˆ (d) 2ˆi +3ˆj + 4kˆ

14. Moment of inertia of a disc about OO’ is

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(a)3mr^2 / 2 (b)mr^2 / 2 (c)5mr^2 / 2 (d)5mr^2 / 4

15. A thin wire of length L and uniform density rho is bent inot a circular loop with center at O as shown.The moment of inertia of the loop about the axis XX’ is

5-15

(a)rho L^3/ 8 pi^2 (b)rho L^3/ 16 pi^2 (c)5 rho L^3/ 16 pi^2 (d)3 rho L^3/ 8 pi^2

16. A rod of mass m and lenth l is kept on a surface that has no friction. if a ball comes & hits the lower end with a velocity v, then the velocity of centre of mass will be:

5-16

(a) zero (b) along negative x-axis
(c) along positive x-axis (d) cannot determine with the given data

17. A body of mass m and radius r is rotated with angular velocity w as shown in the figure & kept on a surface that has sufficient friction then the body will move:

5-17

(a) backward first and then move forward
(b) forward first and then move backward
(c) will always move forward
(d) None of these

18. A uniform circular disc placed on a horizontal rough surface has initially a velocity v0 and an angular velocity W0 as shown in the figure. the disc comes to rest after moving some distance in the direction of motion. Then v0/w0 is:

5-18

(a) r/2 (b) r (c) 3r/2 (d) 2
19. A solid sphere rolls down an inclined plane without slipping. The fraction of its total energy associated with its translation motion is:d
(a) 5/7 (b) 7/10 (c) 2/7 (d) None of these
20. A ring, a disc, a sphere and a spherical shell are simultaneously released to roll down from the top of
an inclined plane of height h. The four bodies will reach the bottom in the following order
(a) sphere, disc, shell and ring (b) ring, spherical shell, disc and sphere
(c) sphere, spherical shell, disc and ring (d) sphere, spherical shell, ring and disc.

21. The capacitance of the capacitors of plate areas A1 and A2 (A1 < A2) at a distance d is

5-21

5-21-ans

22. Two spherical conductors A and B of radii a and b (b > a) are placed concentrically in air. A is given a charge +Q while B is earthed. Then the equivalent capacitance of teh system is

5-22

5-22-ans

23. The capacitors A and B are connected in series with a battery as shown in the figure. When the switch S is closed and the two cpacitors get charged fully, then-

5-23
(a) The potential difference across the plats of A is 4V and
across the plates of B is 6V
(b) The potential difference across the plates of A is 6V and across the plates of B is 4V
(c) The ratio of electric energies stored in A dn B is 2 : 3
(d) The ratio of charges on A and B is 3 : 2

24. Two capacitors of 2μF and 3μF are connected in series. The potential at point A is 1000 volt and the outer plate of 3μF capacitor is earthed. The potential at point B is-

5-24
(a) 300 volt (b) 500 volt (c) 600 volt (d) 400 volt

25. Four plates are arranged as shown in the diagram. If area of each plate is A and the distance between two neighboring  parallel plates is d, then the capacitance of this system will be

5-25

5-25-ans

26. Three capacitors are connected as shown in figure. Then the charge on capacitor plate C1 is-

5-26

(a) 6 μC (b) 12 μC (c) 18 μC (d) 24 μC

27. Two identical capacitors 1 and 2 connected in series to a battery as shown in fig. Capacitor 2 contains a dielectric slab of dielectric constant k as shown. Q1 and Q2 are the charges stored in the capacitors. Now the dielectric slab is removed and the corresponding charges are Q’1 and Q’2. Then

5-27

5-27-ans

28. After charging a capacitor the battery is removed. Now by placing a dielectric slab between the
plates
(a) the potential difference between the plates and the energy stored will decrease but the charge
on plates will remain same
(b) the charge on the plates will decrease and the potentaial difference between the plates will
increase
(c) the plates will remain same
(d) the potential difference, energy stored and the charge will remain unchanged

29. A parallel plate capacitor of plate area A and separation d is filled with two materials each of thickness d/2 and dielectric constants 1  and 2  respectively. The equivalent capacitance will be

 

5-29
(A) E0A/d(E1+E2) (b) (E0A/d)*(E1+E2)/E1E2 (c) (2E0A/d)*E1E2/(E1+E2) (d) (2E0A/d)*(E1+E2)/E1E2

30. A capacitor when charged by a potential difference of 200 volt, stores a charge of 0.1 C. By
discharging, energy liberated by the capacitor is-
(a) –30 J (b) –15 J (c) 10 J (d) 20 J

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