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The angular speed of a body changes from $\omega_{1}$ to $\omega_{2}$ without applying a torque but due to change in its moment of inertia. The ratio of radii of gyration in the two cases is (a) $\sqrt{\omega_{2}}: \sqrt{\omega_{1}}$ (b) $\sqrt{\omega_{1}}: \sqrt{\omega_{2}}$ (c) $\omega_{1}: \omega_{2}$ (d) $\omega_{2}: \omega_{1}$

The angular speed of a body changes from $\omega_{1}$ to $\omega_{2}$ without applying a torque but due to change in its moment of inertia. The ratio of radii of gyration in the two cases is (a) $\sqrt{\omega_{2}}: \sqrt{\omega_{1}}$ (b) $\sqrt{\omega_{1}}: \sqrt{\omega_{2}}$ (c) $\omega_{1}: \omega_{2}$ (d) $\omega_{2}: \omega_{1}$

Objective Physics for NEET

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INSTANT ANSWER

A two-way slab has been shown in the figure. Story height is \( 3.50 \mathrm{~m} \) and beams and columns dimensions are \( 35 \times 50 \mathrm{~cm} \) and \( 35 \times 35 \mathrm{~cm} \) respectively. Service live load is \( 5 \mathrm{kN} / \mathrm{m}^{2} \) and the dead load is assumed only due to the weight of the slab. For the marked panel: 1. Determining the thickness for the panel, 2. Compute the bending moments in different areas of the panel and determine the longitudinal reinforcement of the slab? \( \left(f_{y}=400 \mathrm{MPa}, f_{c}=30 \mathrm{MPa}\right. \) and weight of concrete: \( 24 \mathrm{kN} / \mathrm{m}^{3} \) )

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Numerade educator

1. [20 points] Evaluate the following equations; a) ( delta_{2 j} b_{j}= ) ? b) ( delta_{i j} varepsilon_{i j k}= ) ? c) ( delta_{2 j} A_{i j}= ) ? d) If ( dot{mathbf{u}}_{1}=omega imes mathbf{u}_{1} ) and ( dot{mathbf{u}}_{2}=omega imes mathbf{u}_{2} ) where ( mathbf{u}_{1} ) and ( mathbf{u}_{2} ) are displacement vector and ( omega ) is angular velocity vector. Show that ( frac{d}{d t}left(mathbf{u}_{1} imes mathbf{u}_{2} ight)=omega imesleft(mathbf{u}_{1} imes mathbf{u}_{2} ight) ) Hint: ( mathbf{a} imes(mathbf{b} imes mathbf{c})=mathbf{b}(mathbf{a . c})-mathbf{c}(mathbf{a} . mathbf{b}) )

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JRE P4.29 cube having diagonal \( O C \). determine (a) the unit normal \( \hat{\mathbf{n}} \) for the line element originall of \( \hat{\mathbf{N}}=\left(\hat{\mathbf{I}}_{1}-\hat{\mathbf{I}}_{2}+\hat{\mathbf{I}}_{3}\right) / \sqrt{3} \).

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twely, so that partices in planes parailied to the \( x_{3} X_{3} \) femain in thoe planes, and the square fice ABGH becomes the diamond-staped parallelogram aldy shown below. Ass from the mapping equations and Eq. 46.8 , we see that the deformation gradient \( F \) has the matrix form \[ \left|F_{A}\right|=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & k \\ 0 & k & 1 \end{array}\right] \]

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58. \( 40,1 \mathrm{Il}, \mathrm{IIl} \) VPN - (0) \( [ \).. rr:00 \( + \) \[ x_{1}=\lambda_{1} X_{1}, \quad x_{2}=\lambda_{2} X_{2}, \quad x_{3}=\lambda_{3} X_{3} \] where \( \lambda_{1}, \lambda_{2} \), and \( \lambda_{3} \) are constants. e mow sy cac matile FGURE P4.47A Unit cube having diagonal \( \alpha C \). fGUEF Pa,47B FIGURE P4,47C Unit cube with plare AEC shuled. Determine the relationships among \( \lambda_{2} \lambda_{3} \) and \( \lambda_{3} \) if (a) the length of diagonal \( O C \) remains unchanged (b) the rectangular area \( A B F E \) remains unchanged (c) the triangular area \( A C E \) remains unchanged. * ion by cad inar ue Answer: (a) \( \lambda_{1}^{2}+\lambda_{2}^{2}+\lambda_{3}^{2}=3 \) (b) \( \lambda_{2}\left(\lambda_{1}^{2}+\lambda_{1}^{2}\right)=2 \) (c) \( \lambda_{1}^{2} \lambda_{2}^{2}+\lambda_{2}^{2} \lambda_{5}^{2}+\lambda_{3}^{2} \lambda_{1}^{2}=3 \) 4.48 Let the unit cube shown in Problem 4.47 be given the motion

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\( \rightarrow \quad \) Continuum_mech.pdf URE P4.29 cube having diagonal \( O C \). determine (a) the unit normal \( \hat{\mathbf{n}} \) for the line element originally of \( \hat{\mathbf{N}}=\left(\hat{\mathbf{I}}_{1}-\hat{\mathbf{I}}_{2}+\hat{\mathbf{I}}_{3}\right) / \sqrt{3} \). (b) the stretch \( \Lambda_{(\hat{\mathbf{N}})} \) of this element. (c) the maximum and minimum stretches at the po \( 0, X_{3}=-2 \) in the reference configuration. Answer: (a) \( \hat{\mathbf{n}}=\frac{\sqrt{2} \hat{\mathbf{e}}_{1}+(\sqrt{2}-7) \hat{\mathbf{e}}_{2}+(\sqrt{2}+7) \hat{\mathbf{e}}_{3}}{\sqrt{104}} \) (b) \( \Lambda_{(\hat{\mathbf{N}})}=1.472 \) (c) \( \Lambda_{(\max )}=2 ; \Lambda_{(\min )}=0.5 \)

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