Question

section - a

1. which of the following has unit but no dimension.

a. angle b. strain
c. relative velcoity d. relative density

1. the position-time (x-t) graph for positive acceleration is

a. b.

c. d.

1. the displacement graph of two moving bodies make an angle of 30° and 45° with x-axis the ratio of their velocity is i.e. $v_a:v_b$.

1. a ball strikes a bat with velocity v. the ball has mass m and after striking it retraces its path with save velocity. what is the impulse imparted by the bat?

a. $3mv$ b. $mv$ c. zero d. $2mv$

Explanation:

Step1: Analyze question 1

Quantities with unit but no dimension: Angle has units (radian) but is dimensionless. Strain is dimensionless, no unit; relative velocity has dimension; relative density is dimensionless, no unit.

Step2: Analyze question 2

Positive acceleration: $x-t$ graph's slope (velocity) increases. Graph a has increasing slope, matches positive acceleration.

Step3: Analyze question 3

Velocity = slope of $x-t$ graph.
$V_A = \tan30^\circ = \frac{1}{\sqrt{3}}$, $V_B = \tan45^\circ = 1$
Ratio $V_A:V_B = \frac{1}{\sqrt{3}}:1 = 1:\sqrt{3}$

Step4: Analyze question 4

Impulse = change in momentum.
Initial momentum: $p_i = mV$, final momentum: $p_f = -mV$ (reverse direction)
Change in momentum: $\Delta p = p_f - p_i = -mV - mV = -2mV$, magnitude is $2mv$

Answer:

1. a. angle
2. a. [the upward-curving x-t graph]
3. a. $1:\sqrt{3}$
4. d. $2mv$