Identify the unit vector in the following?

(a)

\(\hat { i } +\hat { j } \)

(b)

\(\frac { \hat { i } }{ \sqrt { 2 } } \)

(c)

\(\hat { k } -\frac { \hat { j } }{ \sqrt { 2 } } \)

(d)

\(\frac { \hat { i } +\hat { j } }{ \sqrt { 2 } } \)

Two objects of masses m₁ and m₂ fall from the heights h₁ and h₂ respectively. The ratio of the magnitude of their momenta when they hit the ground is

(a)

\(\sqrt { \frac { { h }_{ 1 } }{ { h }_{ 2 } } } \)

(b)

\(\sqrt { \frac { { { m }_{ 1 }h }_{ 1 } }{ { { m }_{ 2 }h }_{ 2 } } } \)

(c)

\(\frac { { m }_{ 1 } }{ { m }_{ 2 } } \sqrt { \frac { { h }_{ 1 } }{ { h }_{ 2 } } } \)

(d)

\(\frac { { m }_{ 1 } }{ { m }_{ 2 } } \)

If the velocity is \(\overrightarrow { v } =2\hat { i } +{ t }^{ 2 }\hat { j } -9\overrightarrow { k } \), then the magnitude of acceleration at t = 0.5s is

(a)

1 ms^-2

(b)

2 ms^-2

(c)

zero

(d)

-1 ms^-2

A ball is projected vertically upwards with a velocity v. It comes back to ground in time t. Which v-t graph shows the motion correctly?

(a)

(b)

(c)

(d)

A ball is dropped from some height towards the ground. Which one of the following represents the correct motion of the ball?

(a)

(b)

(c)

(d)