A body of mass \(5\) kg is suspended by the strings making angles $60°$and $30°$with the horizontal.

Then:
a. ${\mathrm{T}}_1=25$ $\mathrm{N}$                    
b. ${\mathrm{T}}_2=25$ $\mathrm{N}$
c. ${\mathrm{T}}_1=25\sqrt{3}$ $\mathrm{N}$               
d. ${\mathrm{T}}_2=25\sqrt{3}$ $\mathrm{N}$
Choose the correct option:

1.	(a), (b)	2.	(a), (d)
3.	(c), (d)	4.	(b), (c)

The banking angle for a curved road of radius \(490\) m for a vehicle moving at \(35\) m/s is:
1. ${\tan }^{-1}(0.25)$
2. ${\tan }^{-1}(0.55)$
3. ${\tan }^{-1}(0.45)$
4. ${\tan }^{-1}(0.75)$

A block of mass \(\mathrm{m}\) is in contact with the cart C as shown in the figure. 
        
The coefficient of static friction between the block and the cart is $\mathrm{\mu }$. The acceleration $\mathrm{\alpha }$ of the cart that will prevent the block from falling satisfies:
1. $\mathrm{\alpha }>\frac{\mathrm{mg}}{\mathrm{\mu }}$

2. $\mathrm{\alpha }>\frac{\mathrm{g}}{\mathrm{\mu m}}$

3. $\mathrm{\alpha }\ge \frac{\mathrm{g}}{\mathrm{\mu }}$

4. $\mathrm{\alpha }<\frac{\mathrm{g}}{\mathrm{\mu }}$

A car of mass \(1000\) kg negotiates a banked curve of radius \(90\) m on a frictionless road. If the banking angle is of \(45^\circ,\) the speed of the car is:

A block \(A\) of mass 7 kg is placed on a frictionless table. A thread tied to it passes over a frictionless pulley and carries a body \(B\) of mass 3 kg at the other end. The acceleration of the system will be: (given \(g\) = 10 ms^–2)

A plank with a box on it at one end is gradually raised at the other end. As the angle of inclination with the horizontal reaches 30°, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank, respectively, will be:
    

The force \(\mathrm{F}\) acting on a particle of mass \(\mathrm{m}\) is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from \(0\) to \(8\) s is:
        

A system consists of three masses \(m_1\), \(m_2\)_, and \(m_3\) connected by a string passing over a pulley \(\mathrm{P}\). The mass \(m_1\) hangs freely, and \(m_2\) and \(m_3\) are on a rough horizontal table (the coefficient of friction = \(\mu\)). The pulley is frictionless and of negligible mass. The downward acceleration of mass \(m_1\) is: (Assume \(m_1=m_2=m_3=m\) and \(g\) is the acceleration due to gravity.) 
             
1. \(\frac{g(1-g \mu)}{9}\)
2. \(\frac{2 g \mu}{3}\)
3. \( \frac{g(1-2 \mu)}{3}\)
4. \(\frac{g(1-2 \mu)}{2}\)

Three blocks \(\mathrm{A}\), \(\mathrm{B}\), and \(\mathrm{C}\) of masses \(4~\text{kg}\), \(2~\text{kg}\), and \(1~\text{kg}\) respectively, are in contact on a frictionless surface, as shown. If a force of \(14~\text{N}\) is applied to the \(4~\text{kg}\) block, then the contact force between \(\mathrm{A}\) and \(\mathrm{B}\) is: 
          
1. \(2~\text{N}\)
2. \(6~\text{N}\)
3. \(8~\text{N}\)
4. \(18~\text{N}\)

A rigid ball of mass \(M\) strikes a rigid wall at \(60^{\circ}\) and gets reflected without loss of speed, as shown in the figure. The value of the impulse imparted by the wall on the ball will be: