Relative Acceleration

Q.

The instantaneous displacement of a simple pendulum oscillator is given by x=Acos (wt+π/4). It's speed will be maximum at time

Q. The accuracy in the measurement of length 50 cm of a simple pendulum is 1 mm. If time period of 2s is determined by measuring the time of 50 oscillations using a watch of resolution 0.2s. The percentage error in the determined value of g is (1) 0.2% (2) 0.3% (3) 0.6% (4) 0.4%

Q.

Two cars A and B are traveling in the same direction with velocities $v_1$ and $v_2(v_1>v_2)$ When the car A is at a distance d ahead of the car B, the driver of the car A applied the brake producing a uniform retardation a. There will be no collision when

1. 
2. 
3. 
4. 

Q. A ball is dropped downward from the roof of a building and simultaneously another ball is thrown in a horizontal direction from the same roof, when and where will the balls reach the ground?

1. Both will reach at same time and same place.

2. The first ball will reach later than the second ball at same place.

3. The second ball will reach later than the first ball at different place.

4. Same time but different places.

Q. If the length and the time period of an oscillating pendulum have errors 1% and 2% respectively. What is the error in the estimate of g?

Q. A car and a truck move in the same straight line at the same instant of time from the same place. The car moves with a constant velocity of $40m/s$ and the truck starts with a constant acceleration of $4m/s^2$. Find the time $t$ that elapses before the truck catches up with the car.

1. $10s$
2. $20s$
3. $30s$
4. $40s$

Q. A boy standing on a long railroad car throws a ball straight upwards. The car is moving on the horizontal road with an acceleration of $1m/s^2$ and the projection speed in the vertical direction in $9.8m/s$. How far the ball will fall behind the boy? $(\text{Take}g=9.8m/s^2)$

1. $4m$
2. $2m$
3. $5m$
4. $1m$

Q. The ratio between the height H of a mountain and the depth h of a mine if a simple pendulum swings with the same period at the top of the mountain and at the bottom of the mine is?

Q.

At the instant the traffic light turns green, an automobile starts with a constant acceleration, $a=10m/s^2.$ At the same instant a truck, travelling with a constant speed of 5 m/s, overtakes and passes the automobile. (a) How far beyond the traffic signal will the automobile overtake the truck? (b) How fast will the automobile be at that instant?

1. 10m, 15 m/s

2. 5m, 10 m/s

3. 10m, 10 m/s

4. 5m, 15 m/s

Q. Two cars ${\text{C}}_1$ and ${\text{C}}_2$ moving in the same direction on a straight single lane road with velocities $12m/s$ and $10m/s$ respectively. When the separation between the two was $200m$, ${\text{C}}_1$ started decelerating to avoid the collision. What is the minimum retardation of car ${\text{C}}_1$ so that they don't collide?

1. $1m/s^2$
2. $1cm/s^2$
3. $0.1m/s^2$
4. $0.01cm/s^2$

Q. Given below are two statements.

Statement $\left(1\right)$ : A second's pendulum has a time period of $1\text{second}$.

Statement $\left(2\right)$ : It takes precisely one second to move between the two extreme positions.

In the light of the above statements, choose the correct answer from the options given below.

1. Both statement $1$ and statement $2$ are false.
2. Statement $1$ is true, but statement $2$ is false.
3. Statement $1$ is false, but statement $2$ is true.
4. Both statement $1$ and statement $2$ are true.

Q. An elevator is moving up with an acceleration $a{\text{m/s}}^2$. A person inside the lift throws the ball upwards with a velocity $u\text{m/s}$ relative to himself. Then the time of flight of ball ($\text{in sec}$) will be:

1. $\frac{u}{g+a}$
   
2. $\frac{u}{g-a}$
   
3. $\frac{2u}{g+a}$
   
4. $\frac{2u}{g-a}$
   

Q. If a ball is thrown up, is the time taken by it for the upward and downward motion equal? Explain.

Q.

Derive an expression for time period of simple pendulum ( for 5marks question)

Q. at what depth from the earths surface the value of acceleration due to gravity reduces by 1% of its value on the earth surface?

Q.

A healthy young man stand at a distance of $7m$ from a $11.8m$height building sees a kid slipping from the top floor. With what speed (assume uniform) should he run to catch the kid at the arm s height at $1.8m$

Q. A stationary body of mass $m$ is slowly lowered onto a rough massive platform moving at a constant velocity $v_0=4\text{m/s}$. If the displacement of the body with respect to the platform $(\mu =0.2)$ is $x\text{m}$, then $x$ is
(Take $g=10{\text{m/s}}^2$)

1. $4$
2. $6$
3. $12$
4. $8$

Q. Two cars ${\text{C}}_1$ and ${\text{C}}_2$ moving in the same direction on a straight single lane road with velocities $12m/s$ and $10m/s$ respectively. When the separation between the two was $200m$, ${\text{C}}_1$ started decelerating to avoid the collision. What is the minimum retardation of car ${\text{C}}_1$ so that they don't collide?

1. $1m/s^2$
2. $1cm/s^2$
3. $0.1m/s^2$
4. $0.01cm/s^2$

Q. Two bodies $A$ and $B$ are thrown simultaneously. $A$ is projected vertically upwards with $80\text{m/s}$ speed from the ground and $B$ is projected vertically downwards from a height of $160\text{m}$ with $40\text{m/s}$ and along the same line of motion. The time taken for the two bodies to collide is

1. $1\text{sec}$
2. $1.33\text{sec}$
3. $2\text{sec}$
4. $1.66\text{sec}$

Q.

A body is thrown vertically upwards. Which one of the following graphs correctly represents the velocity vs time?

1. 

2. 

3. 

4. 

Q.

Car A is moving with a speed of 36 km/h on a two-lane road. Two cars B and C, each moving with a speed of 54 km/h in opposite directions on the other lane are approaching car A. At a certain instant when the distance AB = distance AC = 1 km, the driver of car B decides to overtake A before C does. What must be the minimum acceleration of car B so as to avoid an accident?

1. $1m{s}^{-2}$

2. $2m{s}^{-2}$

3. $3m{s}^{-2}$

4. $4m{s}^{-2}$

Q.

The speedometer of your car shows that you are travelling at a constant speed of $40{\text{ms}}^{-1}$. Is it possible that your car accelerating?

Q.

Two trains simultaneously left points $M$ and $N$ and headed towards each other.

The distance between point $M$ and point $N$ is $380$ mi.

The speed of the train, which started, from point $N$ was $5$mph faster than the speed of the other train.

In two hours after the departure the distance between the trains was $30$ mi.

What is the speed of each train?

Q.

Two particles A and B are thrown vertically upward with velocity, 5 m/s and 10 m/s respectively ($g=10m/s^2$). Find separation between them after one second. (Use relative motion approach)

1. 0 m

2. 5 m

3. 10 m

4. 15 m

Q. A ball is dropped from a height of $20\text{m}$. At the same instant, another ball is thrown upward from the ground with a speed of $20\text{m/s}$ along the same line. After what time will the two balls meet?

1. $4\text{s}$
2. $3\text{s}$
3. $2\text{s}$
4. $1\text{s}$

Q. A small block of wood of specific gravity $0.5$ is submerged at a depth of $1.2m$ in a vessel filled with the water. The vessel is accelerated upwards with an acceleration $a_0=g/2$. Time taken by the block to reach the surface, if it is released with zero initial velocity is

1. $0.6s$
2. $0.4s$
3. $1s$
4. $1.2s$

Q. A body is projected vertically upwards. The times corresponding to height h while ascending and while descending are $t_1$ and $t_2$ respectively. Then the velocity of projection is (g is acceleration due to gravity).

1. $\frac{g\sqrt{t_1{t}_2}}{2}$
2. $\frac{g(t_1+t_2)}{2}$
3. $g\sqrt{t_1{t}_2}$
4. $\frac{g{t}_1{t}_2}{t_1+t_2}$

Q. A student performs an experiment to determine the time period of a pendulum. They obtain the result as $2.53\text{s},2.55\text{s},2.51\text{s},2.52\text{s},2.56\text{s}$. If the actual value for the time period of the pendulum is $1.50\text{s}$, then which of the following statements is true ?

1. Results are precise, but not accurate
2. Results are accurate, but not precise
3. Results are both precise and accurate
4. Results are neither precise not accurate

Q.

I want to play a prank on my friend and turn his world upside down, at what acceleration must his lift move to make it seem that the world is upside down to him

1. g downwards

2. 2g downwards

3. 2g upwards

4. g upwards

Q. As the temperature is increased, the time period of a pendulum
(a) increases proportionately with temperature
(b) increases
(c) decreases
(d) remains constant