A body is at rest at x = 0. At t = 0, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x = 0 moving in the positive x-directionn with a constant speed. The position of the first body is given by x1(t) after time ‘t’ and that of the second body by x2(t) after the same time interval. Which of the following graphs correctly describes (x_{1} – x_{2})as a function of time ‘t’?
B.
A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 kms^{−1}, the escape velocity from the
1.1 kms^{−1}
11 kms^{−1}
110 kms^{−1}
0.11 kms^{−1}
C.
110 kms^{−1}
The dimension of magnetic field in M, L, T and C (Coulomb) is given as
MLT^{−1}C^{−1}
MT^{2}C^{−2}
MT^{−1}C^{−1}
MT^{−2}C^{−1}
C.
MT^{−1}C^{−1}
F = qvB
B = F/qv
= MC^{−1} T^{−1}
Consider a uniform square plate of side ‘a’ and mass ‘m’. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is
(5/6)ma^{2}
(1/12)ma^{2}
(7/12)ma^{2}
(2/3)ma^{2}
D.
(2/3)ma^{2}
Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of − 0.03 mm while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is
3.32 mm
3.73 mm
3.67 mm
3.38 mm
D.
3.38 mm
Diameter = M.S.R. + C.S.R × L.C. + Z.E.
= 3 + 35 × (0.5/50) + 0.03 = 3.38 mm
A block of mass 0.50 kg is moving with a speed of 2.00 m/s on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is
0.16 J
1.00 J
0.67 J
0.34 J
C.
0.67 J
m_{1}u_{1} + m_{2}u_{2} = (m_{1} + m_{2})v
v = 2/3 m/s
An athlete in the Olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range
200 J − 500 J
2 × 105J ^{− 3} × 105J
20,000 J − 50,000 J
2,000 J − 5,000 J
C.
20,000 J − 50,000 J
Approximate mass = 60 kg Approximate
velocity = 10 m/s Approximate
KE = (1/2)x60 x1000 = 3000 J
= KE range ⇒ 2000 to 5000 joule
This question contains Statement -1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement – I:
For a mass M kept at the centre of a cube of side ‘a’, the flux of gravitational field passing through its sides is 4π GM.
and
Statement – II
If the direction of a field due to a point source is radial and its dependence on the distance ‘r’ for the source is given as 1/r_{2}, its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface
Statement – 1is false, Statement – 2 is true.
Statement – 1is true, Statement – 2 is true; Statement -2 is correct explanation for Statement-1.
Statement – 1 is true, Statement – 2 is true; Statement -2 is not a correct explanation for Statement-1.
Statement – 1 is true, Statement – 2 is False.
B.
Statement – 1is true, Statement – 2 is true; Statement -2 is correct explanation for Statement-1.
g = GM/r^{2}
A thin rod of length ‘L’ is lying along the x-axis with its ends at x = 0 and x = L. Its linear density (mass/length) varies with x as, where n can be zero or any positive number. If the position x_{CM} of the centre of mass of the rod is plotted against ‘n’, which of the following graphs best approximates the dependence of x_{CM} on n?
A.
A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms^{−1}.The magnitude of its momentum is recorded as
17.6 kg ms^{−1 }
17.565 kg ms^{−1}
17.56 kg ms^{−1}
17.57 kg ms^{−1}
A.
17.6 kg ms^{−1 }
P = mv = 3.513 × 5.00 ≈ 17.6
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