Q76
Allen
4. JEE-Advanced Pattern
Numerical
A body starting from rest accelerates uniformly at the rate of $10 \, cm s^{-2}$ and retards uniformly at the rate of $20 \, cm/sec^{2}$ . Find the least time in which it can complete a journey of 5 km if the maximum velocity attained by the body is $72 \, km/h^{-1}$ .
Correct Answer: 400
Explanation:
Ans. (400) $u = 0, \alpha = 10cm / s^2, \beta = 20cm / s^2$ $5km = \frac{1}{2} \times t \times v_m$ $t = \alpha v_0 + \beta v_0$
Q77
Allen
4. JEE-Advanced Pattern
Numerical
A ball is thrown vertically upwards from the ground. It crosses a point at the height of 25 m twice at an interval of 4 secs. The ball was thrown with the velocity of
Correct Answer: 30
Explanation:
Ans. (30)
$V = 10(2)$ $= 20m / s$ $v^{\prime 2} = 20^{2} + 2\times 10\times 25$ $= 400 + 500$ $= 900$ $v^{\prime} = 30m / s$ Ans.
$V = 10(2)$ $= 20m / s$ $v^{\prime 2} = 20^{2} + 2\times 10\times 25$ $= 400 + 500$ $= 900$ $v^{\prime} = 30m / s$ Ans.
Q78
Allen
4. JEE-Advanced Pattern
Match the Columns
A small ball is projected along the surface of a smooth inclined plane with speed 10m/s along the direction shown at t = 0. The point of projection is origin, z-axis is along vertical. The acceleration due to gravity is $10 \, m/s^{2}$ . Column-I lists values of certain parameters related to motion of ball and column-II lists different time instants. Match appropriately.
| Column-I | Column-II | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
Correct Answer: (A-P,R), (B-Q), (C-S)
Explanation:
Ans. (A-P,R), (B-Q), (C-S)
Considering y-axis along the inclined plane
Time of flight $= \frac{2u\sin37^{\circ}}{g\sin37^{\circ}} = 2s$
Speed is minimum at t = 1s
Velocity makes an angle $37^{\circ}$ at $t = 2$
$y = 6 t - \frac {1}{2} g \sin 3 7 ^ {\circ} t ^ {2}$
Substituting $y = 2.25$
We get t = 0.5 and 1.5s
Considering y-axis along the inclined plane
Time of flight $= \frac{2u\sin37^{\circ}}{g\sin37^{\circ}} = 2s$
Speed is minimum at t = 1s
Velocity makes an angle $37^{\circ}$ at $t = 2$
$y = 6 t - \frac {1}{2} g \sin 3 7 ^ {\circ} t ^ {2}$
Substituting $y = 2.25$
We get t = 0.5 and 1.5s
Q79
Allen
4. JEE-Advanced Pattern
Match the Columns
v, a, s and t denote velocity, acceleration, displacement and time respectively. Match the columns :-
| Column-I | Column-II | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
Correct Answer: (A-R,T), (B-T), (C-R,T), (D-S,T)
Explanation:
Ans. (A-R,T), (B-T), (C-R,T), (D-S,T)
(A)
(B)
(C)
(D)
(A)
(B)
(C)
(D)
Q80
Allen
4. JEE-Advanced Pattern
Match the Columns
Column-I
| Column-I | Column-II | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
Correct Answer: (A-P,Q), (B-R), (C-S), (D-P,R)
Explanation:
Ans. (A-P,Q), (B-R), (C-S), (D-P,R)
(A)
(B)
(C)
$t = \frac {\ell}{| \bar {v} |}\tag{D}$
$t = \frac {\ell}{| \bar {v} + \bar {u} |} = \frac {\ell}{| \bar {v} | + | \bar {u} |}$
(A)
(B)
(C)
$t = \frac {\ell}{| \bar {v} |}\tag{D}$
$t = \frac {\ell}{| \bar {v} + \bar {u} |} = \frac {\ell}{| \bar {v} | + | \bar {u} |}$