The quantity which has the same dimensions as that of gravitational potential is
latent heat
impulse
angular acceleration
Planck's constant
The percentage error in measuring M, L and T are 1 %, 1.5% and 3% respectively. Then the percentage error in measuring the physical quantity with dimensions [ML-1 T-1] is
1 %
3.5 %
5.5 %
4.5 %
From an elevated point P, a stone is projected vertically upwards when the stone reaches a distance h below P, its velocity is double of its velocity at a height h above P. The greatest height attained by the stone from the point of projection is
B.
From equations of motions, we know
v2 = u2 − 2gh ......... (i)
Here, v = 2v,so
(2v)2 = u2 + 2gh ......... (ii)
Now, on adding Eqs. (i) and (ii), we get
5v2 = 2u2
u2 = ......... (iii)
On subtracting Eq. (i) in Eq. (ii), we get
3v2 = 4gh
v2 = ......... (iv)
And we know that the,
So, here,
The distance x covered by a particle varies with time t as x2 = 2t2 + 6t + 1. Its acceleration varies with x as
x
x2
x-1
x-3
A particle describes uniform circular motion in a circle of radius 2 m, with the angular speed of 2 rad s-1. The magnitude of the change in its velocity in s is
0 ms-1
8 ms-1
4 ms-1
A body projected at an angle with the horizontal has a range 300 m. If the time of flight is 6 s, then the horizontal component of velocity is
30 ms-1
50 ms-1
40 ms-1
45 ms-1
A constant force F acts on a particle of mass 1 kg moving with a velocity v, for one second. The distance moved in that time is
0
2F
The velocity-time graph for the vertical component of the velocity of a body thrown upwards from the ground and landing on the roof of a building is given in the figure. The height of the building is
50 m
40 m
20 m
30 m
A spacecraft of mass 100 kg breaks into two when its velocity is 104 ms-1. After the break, a mass of 10 kg of the spacecraft is left stationary. The velocity of the remaining part is
103 ms-1
11.11 × 103 ms-1
11.11 × 102 ms-1
104 ms-1
A particle tied to a string describes a vertical circular motion of radius r continually. If it has a velocity at the highest point, then the ratio of the respective tensions in the string holding it at the highest and lowest points is
4 : 3
5 : 4
1 : 4
3 : 2