In a simple pendulum experiment, the maximum percentage error in the measurement of length is 2% and that in the observation of the time-period is 3%. Then, the maximum percentage error in determination of the acceleration due to gravity g is

• 5 %

• 6 %

• 7 %

• 8 %

The pitch and the number of circular scale divisions in a screw gauge with least count 0.02 mm are respectively

• 1 mm and 100

• 0.5 mm and 50

• 1 mm and 50

• 0.5 mm and 100

A ball is dropped from the top of a tower of height 100 m and at the same time another ball is projected vertically upwards from ground with a velocity 25 ms^-1. Then, the distance from the top of the tower, at which the two balls meet is

• 68.4 m

• 48.4 m

• 78.4 m

• 18.4 m

The ratio of distance traversed in successive intervals of time when a body falls freely under gravity from certain height is

• 1 : 2 : 3

• 1 : 5 : 9

• 1 : 3 : 5

• $\sqrt{1} : \sqrt{2} : \sqrt{3}$

A particle starting with certain initial velocity and uniform acceleration covers a distance of 12 m in first 3 s and a distance of 30 m in next 3 s. The initial velocity of the particle is

• 3 ms^-1

• 2.5 ms^-1

• 1 ms^-1

• 1.5 ms^-1

A ball of mass 10 g moving perpendicular to the plane of the wall strikes it and rebounds in the same line with the same velocity. If the impulse experienced by the wall is 0.54 Ns, the velocity of the ball is

• 27 ms^-1

• 3.7 ms^-1

• 54 ms^-1

• 37 ms^-1

7.

A particle has the position vector $\mathrm{r} = \hat{\mathrm{i}} - 2\hat{\mathrm{j}} + \hat{\mathrm{k}}$ and the linear momentum $\mathrm{p} = 2\hat{\mathrm{i}} - \hat{\mathrm{j}} + \hat{\mathrm{k}}$. Its angular momentum about the origin is

• $- \hat{\mathrm{i}} + \hat{\mathrm{j}} - 3\hat{\mathrm{k}}$

• $- \hat{\mathrm{i}} + \hat{\mathrm{j}} + 3\hat{\mathrm{k}}$

• $\hat{\mathrm{i}} - \hat{\mathrm{j}} + 3\hat{\mathrm{k}}$

• $\hat{\mathrm{i}} - \hat{\mathrm{j}} - 5\hat{\mathrm{k}}$

The vertical component of velocity of a projectile at its maximum height (u = velocity of projection, θ = angle of projection) is

• u sin θ

• u cos θ

• $\frac{\mathrm{u}}{\sin \mathrm{\theta }}$

• zero

The coordinates of a particle moving in x-y plane at any instant of time t are x = 4t² ; y = 3t². The speed of the particle at that instant is

• 10t

• 5t

• 3t

• 2t

A cyclist bends while taking turn in order to

• reduce friction

• provide required centripetal force

• reduce apparent weight

• reduce speed