Problem Solving

Q. a=x^2 find velocity when x is 2 m given at x=0 body is at rest

Q.

The maximum speed of a particle executing S.H.M. is 1m/s and its maximum acceleration is 1.57m/$se{c}^2$ . The time period of the particle will be

[DPMT 2002]

1. 

2. 1.57 sec

3. 2 sec

4. 4 sec

Q. A ball of mass m hits a floor with a speed v making an angle a with the normal N. The coefficient of restitution is e. The angle made by reflected ball with floor is N V (1) cot (ecota) (2) tan (ecota) e (4) Cot1 tan o (3) tan 1/ tan

Q.

A bullet comes out of the barrel of gun of length $2m$ with a speed $80m/s$. The average acceleration of the bullet is

1. $1.6m/s^2$

2. $160m/s^2$

3. $1600m/s^2$

4. $16m/s^2$

Q. The direction of three forces 10N, 20N, 30N acting at a point are parallel to sides of an equilateral triangle taken in order.The magnitude of their resul†an t is?

Q. In the figure shown the acceleration of $A$ is ${\overrightarrow{a}}_A=15\hat{i}+15\hat{j}$, then the acceleration of $B$ is ($A$ remains in contact with $B$ ).

1. $6\hat{i}$
2. $-15\hat{i}$
3. $-10\hat{i}$
4. $-5\hat{i}$

Q. A stone is thrown with a velocity v making an anglee with the horizontal. At some instant, its velocityV is perpendicular to the initial velocity v. Then, V is (1) v sin theta (2) v cos theta (3) v tan theta(4) v cot thet

Q. if v is the velocity of a body moving along x-axis, then acceleration of body is

Q.

A body moves according to the formula$v=1+t^2$ where $v$ is the velocity at time $t$. The acceleration after $3sec$ will be ($vincm/sec$)

1. $24cm/se{c}^2$

2. $12cm/se{c}^2$

3. $6cm/se{c}^2$

4. None of these

Q.

A car when passes through a convex bridge exerts a force on it which is equal to

1. $mg+\frac{m{v}^2}{r}$

2. $\frac{m{v}^2}{r}$

3. $Mg$

4. None of these

Q.

A car moves at a constant speed on a road as shown in figure. The normal force by the road on the car is N_A and N_B when it is at the points A and B respectively. Then?

1. N_A< N_B

2. Insufficient information to decide the relation of N_A and N_B.

3. N_A = N_B

4. N_A> N_B

Q.

A bird is sitting on the floor of a closed glass cage in the hands of girls. Will the girl experience any change in the weight of the cage when the bird (i) starts flying in the cage with a constant velocity ? (ii) flies upwards with acceleration ? (iii) flies downwards with acceleration?

Q. { 1. A block of mass }2 kg rests on an inclined plane }}{ of inclination angle }37^° , then calculate the force of }}{ friction acting on the block [take } g = 10 m / s ^ { 2 } \rbrack

Q. Find the acceleration of a system consisting of a solid cylinder of mass $m$ and radius $R$ and a plank of mass $M$ placed on a smooth surface if it is pulled with a force $F$ as shown in the figure. Given that sufficient friction is present between the cylinder and the plank surface to prevent sliding of the cylinder.

1. $\frac{F}{m+M}$
2. $\frac{F}{2m+M}$
3. $\frac{F}{m+2M}$
4. $\frac{F}{3m+M}$

Q. find range of projectile when equation of trajectory is given by y=ax-bx^2

Q. 26.A body is in pure rotation. The linear speed v of a particle , the distance r of the particle from the axis and the angular velocity w(omega) of the body are related as w(omega) = v/r. Thus (a) omega is directly proportional to 1/r (b) omega directly proportional to r (c) omega = 0 (d) omega is independent of r. and why?

Q. In the figure, accelerations of blocks $A$, $B$ and $C$ are indicated by $a$, $b$, and $c$ respectively. Acceleration $b$ and $c$ are w.r.t to the ground. Find the acceleration of the body $A$ in terms of $b$ and $c$ with respect to the ground if the surface is smooth and pulley and string is ideal.

1. $\sqrt{(b+c{)}^2+a^2}$
2. $c-(a+b)\cos \theta$
3. $\sqrt{(b+c{)}^2+c^2-2(b+c).c.\cos \theta }$
4. $\sqrt{(b+c{)}^2+c^2+2(b+c).c.\cos \theta }$

Q. A block is placed on a rough inclined plane which is fixed in an elevator. The angle of inclination is θ = tan–1(μ), where μ is coefficient of friction between block and the inclined plane. The elevator is accelerated vertically upwards with an acceleration a. The acceleration of the block w.r.t. inclined plane will be

Q.

A body of mass $2\mathrm{kg}$ is suspended on a spring balance hung vertically in a lift. If the lift is falling downward under acceleration due to gravity g, then what will be the reading of the balance? If going upward with the same acceleration, then?

Q.

The maximum speed at which a car can turn round a curve of 400 m radius on a level road is: (Given: coefficient of friction between the tyres and road is 0.1, and g = 10 m/s²)

1. 26 m/s

2. 20 m/s

3. 14 m/s

4. 21 m/s

Q. { A uniform thin rod of length }( and } mass }m is hinged }} at one end }O and released from horizontal position } as shown in figure. The angular acceleration of } the rod about the hinge point, } when rod becomes } ulvertical is }0

Q. 24.Two fixed frictionless inclined plane making anangle 30^° and 60 with the vertical are shown inthe figure. Two blocks A and B are placed on thetwo planes then what is the relative verticalcomponent of acceleration of A with respectto B:30^°(2) 9.8 m/s2(4) 4.9 m/s260^°(1) 19.6 m/s2(3) Zero

Q. velocity v of an object varies with position x as v=x^2 what ia acceleration of object when the slope of v-x curve is equal to one

Q. Which of the following statement is not correct regarding Newton’s third law of motion?

न्यूटन की गति के तृतीय नियम के संदर्भ में, निम्नलिखित में से कौनसा कथन सही नहीं है?

1. To every action there is equal and opposite reaction
   
   प्रत्येक क्रिया की बराबर व विपरीत प्रतिक्रिया होती है
   
2. Action and reaction act on different bodies
   
   क्रिया तथा प्रतिक्रिया भिन्न-भिन्न पिण्डों पर कार्य करती हैं
   
3. Action and reaction act simultaneously
   
   क्रिया तथा प्रतिक्रिया एकसाथ कार्य करती हैं
   
4. Action and reaction act in same direction
   
   क्रिया तथा प्रतिक्रिया समान दिशा में कार्य करती हैं
   

Q. The electric potential at the centre of hemisphere of radius $R$ having uniform surface charge density $\sigma$ is

1. $\frac{\sigma R}{{ϵ}_0}$
2. $\frac{2\sigma R}{{ϵ}_0}$
3. $\frac{\sigma R}{2{ϵ}_0}$
4. $\frac{\sigma R}{3{ϵ}_0}$

Q. 38. uniform solid cylinder rolls up an incline plane of inclination 30º. At the bottom of the incline plane, the cylinder is given an initial velocity of 5 m/sec. along with the angular velocity required for perfect rolling. How much time will it take to return to the bottom?

Q. The speed of block $A$ in the system shown in the figure is (String is massless and inextensible)

1. $4\text{m/s}$
2. $6\text{m/s}$
3. $8\text{m/s}$
4. $10\text{m/s}$

Q.
The figure shows the force versus time graph for a particle. Then

1. Change in momentum of the particle is $20\text{N-s}$
2. Average force acting on the particle is $50\text{N}$
3. Change in momentum of the particle is $50\text{N-s}$
4. Average force acting on the particle is $20\text{N}$

Q. A particle is resting on a smooth horizontal floor. At $t=0$, a horizontal force starts acting on it. The magnitude of the force increases with time according to law $F=\alpha t$, where $\alpha$ is a constant. For the figure shown which of the following statement is wrong?

1. $\text{Curve 1 shows acceleraion against time}$
2. $\text{Curve 2 shows velocity against time}$
3. $\text{Curve 2 shows velocity against acceleration}$
4. $\text{Curve 1 shows acceleration against velocity}$

Q. The velocity time graph of a lift moving upwards has been shown below. Let $T_1,T_2$ and $T_3$ be the tensions in the elevator cable during the three time intervals $\Delta t_1,\Delta t_2$ and $\Delta t_3$, then $T_1:T_2:T_3$

1. $11:10:9$
2. $19:10:11$
3. $11:10:12$
4. $11:10:8$