Each of three blocks P,Q and R shown in the f | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the mass of each block be $m = 3 \,kg$. The total mass of the system is $3m = 9 \,kg$.The driving force is the weight of block $R$,which is $F

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(D) Let the mass of each block be $m = 3 \,kg$. The total mass of the system is $3m = 9 \,kg$.The driving force is the weight of block $R$,which is $F = mg = 3 	imes 10 = 30 \,N$.The acceleration of the system is $a = \frac{F}{	ext{total mass}} = \frac{30}{3m} = \frac{30}{9} = \frac{10}{3} \,m/s^2$.Wire $B$ connects block $R$ to block $Q$. The tension $T_1$ in wire $B$ can be found by considering the motion of block $R$:$mg - T_1 = ma$$30 - T_1 = 3 	imes \frac{10}{3} = 10$$T_1 = 30 - 10 = 20 \,N$.The stress in wire $B$ is $\sigma = \frac{T_1}{A}$,where $A = 0.005 \,cm^2 = 0.005 	imes 10^{-4} \,m^2 = 5 	imes 10^{-7} \,m^2$.$\sigma = \frac{20}{5 	imes 10^{-7}} = 4 	imes 10^7 \,N/m^2$.The longitudinal strain is $\epsilon = \frac{\sigma}{Y} = \frac{4 	imes 10^7}{2 	imes 10^{11}} = 2 	imes 10^{-4}$.Thus,the strain is $2 	imes 10^{-4}$.

Column $I$	Column $II$
$A$. Hooke's law	$1$. Tangential strain
$B$. Shearing strain	$2$. Temporary loss of elastic property
$C$. Bulk strain	$3$. Elastic limit
$D$. Elastic fatigue	$4$. $3$ times the linear strain

List-$I$	List-$II$
$A$. Young's Modulus	$I$. $\frac{Ad}{\Delta L}$
$B$. Compressibility	$II$. $\frac{FL}{A\Delta L}$
$C$. Bulk Modulus	$III$. $-\frac{1}{\Delta P}(\frac{\Delta V}{V})$
$D$. Poisson's Ratio	$IV$. $-\frac{\Delta D/D}{\Delta L/L}$

Similar Questions

For the tensile stress on the cross-section $PQRS$ to be maximum,$\theta =$ ......... $^o$

Match the following:
Column $I$ Column $II$
$A$. Hooke's law $1$. Tangential strain
$B$. Shearing strain $2$. Temporary loss of elastic property
$C$. Bulk strain $3$. Elastic limit
$D$. Elastic fatigue $4$. $3$ times the linear strain

Match List-$I$ with List-$II$:

List-$I$ List-$II$

$A$. Young's Modulus $I$. $\frac{Ad}{\Delta L}$

$B$. Compressibility $II$. $\frac{FL}{A\Delta L}$

$C$. Bulk Modulus $III$. $-\frac{1}{\Delta P}(\frac{\Delta V}{V})$

$D$. Poisson's Ratio $IV$. $-\frac{\Delta D/D}{\Delta L/L}$

Two blocks of masses $1 \,kg$ and $2 \,kg$ are connected by a metal wire going over a smooth pulley. The breaking stress of metal is $\frac{40}{3 \pi} \times 10^6 \,N m^{-2}$. What should be the minimum radius of the wire used if it should not break (in $mm$)? $(g = 10 \,m s^{-2})$

Vedclass Test Series

Exam Paper Generator

Online Exam Module